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Tesi sul tema "Dynamical Systems"

Autore: Grafiati
Pubblicato: 4 giugno 2021
Ultima modifica: 25 luglio 2025

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1

Behrisch, Mike, Sebastian Kerkhoff, Reinhard Pöschel, Friedrich Martin Schneider, and Stefan Siegmund. "Dynamical Systems in Categories." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-129909.

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Abstract (sommario):
In this article we establish a bridge between dynamical systems, including topological and measurable dynamical systems as well as continuous skew product flows and nonautonomous dynamical systems; and coalgebras in categories having all finite products. We introduce a straightforward unifying definition of abstract dynamical system on finite product categories. Furthermore, we prove that such systems are in a unique correspondence with monadic algebras whose signature functor takes products with the time space. We substantiate that the categories of topological spaces, metrisable and uniformi
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2

Zaks, Michael. "Fractal Fourier spectra in dynamical systems." Thesis, [S.l.] : [s.n.], 2001. http://pub.ub.uni-potsdam.de/2002/0019/zaks.ps.

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3

Haydn, Nicolai Theodorus Antonius. "On dynamical systems." Thesis, University of Warwick, 1986. http://wrap.warwick.ac.uk/55813/.

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Abstract (sommario):
Part A. We prove existence of smooth invariant circles for area preserving twist maps close enough to integrable using renormalisation. The smoothness depends upon that of the map and the Liouville exponent of the rotation number. Part B. Ruelle and Capocaccia gave a new definition of Gibbs states on Smale spaces. Equilibrium states of suitable function there on are known to be Gibbs states. The converse in discussed in this paper, where the problem is reduced to shift spaces and there solved by constructing suitable conjugating homeomorphisms in order to verify the conditions for Gibbs states
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4

Miles, Richard Craig. "Arithmetic dynamical systems." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323222.

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5

Che, Dzul-Kifli Syahida. "Chaotic dynamical systems." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3410/.

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Abstract (sommario):
In this work, we look at the dynamics of four different spaces, the interval, the unit circle, subshifts of finite type and compact countable sets. We put our emphasis on chaotic dynamical system and exhibit sufficient conditions for the system on the interval, the unit circle and subshifts of finite type to be chaotic in three different types of chaos. On the interval, we reveal two weak conditions’s role as a fast track to chaotic behavior. We also explain how a strong dense periodicity property influences chaotic behavior of dynamics on the interval, the unit circle and subshifts of finite
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6

Hillman, Chris. "Sturmian dynamical systems /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5806.

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7

Umenberger, Jack. "Convex Identifcation of Stable Dynamical Systems." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/17321.

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Abstract (sommario):
This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particu
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8

Freeman, Isaac. "A modular system for constructing dynamical systems." Thesis, University of Canterbury. Mathematics, 1998. http://hdl.handle.net/10092/8888.

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Abstract (sommario):
This thesis discusses a method based on the dual principle of Rössler, and developed by Deng, for systematically constructing robust dynamical systems from lower dimensional subsystems. Systems built using this method may be modified easily, and are suitable for mathematical modelling. Extensions are made to this scheme, which allow one to describe a wider range of dynamical behaviour. These extensions allow the creation of systems that reproduce qualitative features of the Lorenz Attractor (including bifurcation properties) and of Chua's circuit, but which are easily extensible.
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9

Ozaki, Junichi. "Dynamical quantum effects in cluster dynamics of Fermi systems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199083.

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10

CAPPELLINI, VALERIO. "QUANTUM DYNAMICAL ENTROPIES AND COMPLEXITY IN DYNAMICAL SYSTEMS." Doctoral thesis, Università degli studi di Trieste, 2004. http://thesis2.sba.units.it/store/handle/item/12545.

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2002/2003<br>We analyze the behavior of two quantum dynamical entropies in connection with the classical limit. Using strongly chaotic classical dynamical systems as models (Arnold Cat Maps and Sawtooth Maps), we also propose a discretization procedure that resembles quantization; even in this case, studies of quantum dynamical entropy production are carried out and the connection with the continuous limit is explored. In both case (quantization and discretization) the entropy production converge to the Kolmogorov-Sinai invariant on time-scales that are logarithmic in the quantization
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11

McKee, Andrew. "Multipliers of dynamical systems." Thesis, Queen's University Belfast, 2017. https://pure.qub.ac.uk/portal/en/theses/multipliers-of-dynamical-systems(65b93a06-6e7b-420b-ae75-c28d373f8bdf).html.

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Herz–Schur multipliers of a locally compact group have a well developed theory coming from a large literature; they have proved very useful in the study of the reduced C∗-algebra of a locally compact group. There is also a rich connection to Schur multipliers,which have been studied since the early twentieth century, and have a large number of applications. We develop a theory of Herz–Schur multipliers of a C∗-dynamical system, extending the classical Herz–Schur multipliers, making Herz–Schur multiplier techniques available to study a much larger class of C∗-algebras. Furthermore, we will also
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12

Hook, James Louis. "Topics in dynamical systems." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/topics-in-dynamical-systems(427b5d98-197d-4b53-876e-a81142f72375).html.

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Abstract (sommario):
In this thesis I explore three new topics in Dynamical Systems. In Chapters 2 and 3 I investigate the dynamics of a family of asynchronous linear systems. These systems are of interest as models for asynchronous processes in economics and computer science and as novel ways to solve linear equations. I find a tight sandwich of bounds relating the Lyapunov exponents of these asynchronous systems to the eigenvalue of their synchronous counterparts. Using ideas from the theory of IFSs I show how the random behavior of these systems can be quickly sampled and go some way to characterizing the assoc
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13

Hua, Xinhou. "Dynamical systems and wavelets." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6143.

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Abstract (sommario):
The first part of this thesis is concerned with Bakers Conjecture (1984) which says that two permutable transcendental entire functions have the same Julia set. To this end, we shall exhibit that two permutable transcendental entire functions of a certain type have the same Julia set. So far, this is the best result to the conjecture. The second part relates to Newton's method to find zeros of functions. We shall look for the locations of the limits of the iterating sequence of the relaxed Newton function on its wandering domains. A relaxed Newton function with corresponding properties is cons
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14

Dam, Albert Anton ten. "Unilaterally constrained dynamical systems." [S.l : [Groningen] : s.n.] ; [University Library Groningen] [Host], 1997. http://irs.ub.rug.nl/ppn/159407869.

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15

Schinkel, Michael. "Nondeterministic hybrid dynamical systems." Thesis, University of Glasgow, 2002. http://theses.gla.ac.uk/1853/.

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Abstract (sommario):
This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world s
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16

Chan, N. "Dynamical systems in cosmology." Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1348375/.

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Abstract (sommario):
In this PhD thesis, the role of dynamical systems in cosmology has been studied. Many systems and processes of cosmological interest can be modelled as dynamical systems. Motivated by the concept of hypothetical dark energy that is believed to be responsible for the recently discovered accelerated expansion of the universe, various dynamical dark energy models coupled to dark matter have been investigated using a dynamical systems approach. The models investigated include quintessence, three-form and phantom fields, interacting with dark matter in different forms. The properties of these model
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17

Krcelic, Khristine M. "Chaos and Dynamical Systems." Youngstown State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1364545282.

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18

Royals, Robert. "Arithmetic and dynamical systems." Thesis, University of East Anglia, 2015. https://ueaeprints.uea.ac.uk/57191/.

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Abstract (sommario):
In this thesis we look at a number of topics in the area of the interaction between dynamical systems and number theory. We look at two diophantine approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly perturbed rational functions. In particular we prove that for a finite set of primes S that the power series f(z) generated by the Fibonacci series with all primes in S removed has a natural boundary.
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19

Hayden, Kevin. "Modeling of dynamical systems /." abstract and full text PDF (UNR users only), 2007. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1446796.

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Abstract (sommario):
Thesis (M.S.)--University of Nevada, Reno, 2007.<br>"May, 2007." Includes bibliographical references (leaves 128-129). Library also has microfilm. Ann Arbor, Mich. : ProQuest Information and Learning Company, [2008]. 1 microfilm reel ; 35 mm. Online version available on the World Wide Web.
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20

Sun, Hongyan. "Coupled nonlinear dynamical systems." Morgantown, W. Va. : [West Virginia University Libraries], 2000. http://etd.wvu.edu/templates/showETD.cfm?recnum=1636.

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Abstract (sommario):
Thesis (Ph. D.)--West Virginia University, 2000.<br>Title from document title page. Document formatted into pages; contains xi, 113 p. : ill. (some col.). Includes abstract. Includes bibliographical references.
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21

Tse, Pak-hoi Isaac. "Dynamical systems theory and school change." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37626218.

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22

Tse, Pak-hoi Isaac, and 謝伯開. "Dynamical systems theory and school change." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37626218.

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23

Kuhlman, Christopher James. "Generalizations of Threshold Graph Dynamical Systems." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/76765.

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Abstract (sommario):
Dynamics of social processes in populations, such as the spread of emotions, influence, language, mass movements, and warfare (often referred to individually and collectively as contagions), are increasingly studied because of their social, political, and economic impacts. Discrete dynamical systems (discrete in time and discrete in agent states) are often used to quantify contagion propagation in populations that are cast as graphs, where vertices represent agents and edges represent agent interactions. We refer to such formulations as graph dynamical systems. For social applications, thresho
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24

Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.

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Abstract (sommario):
Modern complex dynamical systems typically possess a multiechelon hierarchical hybrid structure characterized by continuous-time dynamics at the lower-level units and logical decision-making units at the higher-level of hierarchy. Hybrid dynamical systems involve an interacting countable collection of dynamical systems defined on subregions of the partitioned state space. Thus, in addition to traditional control systems, hybrid control systems involve supervising controllers which serve to coordinate the (sometimes competing) actions of the lower-level controllers. A subclass of hybrid dynamic
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25

Shadden, Shawn Christopher Marsden Jerrold E. "A dynamical systems approach to unsteady systems /." Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05122006-083011.

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26

Schneider, Judith. "Dynamical structures and manifold detection in 2D and 3D chaotic flows." Phd thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=973637420.

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27

Gil, Gibin. "Hybrid Numerical Integration Scheme for Highly Oscillatory Dynamical Systems." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/306771.

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Abstract (sommario):
Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the compu
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28

Zhao, Zhenyuan. "Dynamical Grouping in Complex Systems." Scholarly Repository, 2010. http://scholarlyrepository.miami.edu/oa_dissertations/498.

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Abstract (sommario):
Quantifying the behavior of complex systems arguably presents the common ¡°hard¡±problem across the physical, biological, social, economic sciences. Individual-based or agent-based models have proved useful in a variety of different real world systems: from the physical, biological, medical domains through to social and even financial domains. There are many different models in each of these fields, each with their own particular assumptions, strengths and weaknesses for particular application areas. However, there is a lack of minimal model analysis in which both numerical and analytic result
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29

Badar, Muhammad. "Dynamical Systems Over Finite Groups." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17948.

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In this thesis, the dynamical system is used as a function on afinite group, to show how states change. We investigate the'numberof cycles' and 'length of cycle' under finite groups. Using grouptheory, fixed point, periodic points and some examples, formulas tofind 'number of cycles' and 'length of cycle' are derived. Theexamples used are on finite cyclic group Z_6 with respectto binary operation '+'. Generalization using finite groups ismade. At the end, I compared the dynamical system over finite cyclic groups with the finite non-cyclic groups and then prove the general formulas to find 'num
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30

Newman, Julian. "Synchronisation in random dynamical systems." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/39569.

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Abstract (sommario):
In this thesis, we develop a deeper and much more extensive theory of synchronisation of trajectories of random dynamical systems (RDS) than currently exists. In particular, focusing on random dynamical systems with memoryless noise, we achieve two main goals: Firstly, we demonstrate that the notion of "statistical equilibria" is purely a property of the measurable dynamics of a RDS on a standard Borel space; and yet, within such statistical equilibria is "encoded" the phenomenon of noise-induced synchronisation (which may then be observed in *any* compatible metric on the phase space). Second
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31

Hendtlass, Matthew Ralph John. "Aspects of Constructive Dynamical Systems." Thesis, University of Canterbury. Mathematics and Statistics, 2009. http://hdl.handle.net/10092/2724.

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We give a Bishop-style constructive analysis of the statement that a continuous homomorphism from the real line onto a compact metric abelian group is periodic; constructive versions of this statement and its contrapositive are given. It is shown that the existence of a minimal period in general is not derivable, but the minimal period is derivable under a simple geometric condition when the group is contained in two dimensional Euclidean space. A number of results about one-one and injective mappings are proved en route to our main theorems. A few Brouwerian examples show that some of our res
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32

Ozik, Jonathan. "Evolution of discrete dynamical systems." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2351.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.<br>Thesis research directed by: Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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33

Ertem, Turker. "Asymptotic Integration Of Dynamical Systems." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615405/index.pdf.

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Abstract (sommario):
In almost all works in the literature there are several results showing asymptotic relationships between the solutions of x&prime<br>&prime<br>= f (t, x) (0.1) and the solutions 1 and t of x&prime<br>&prime<br>= 0. More specifically, the existence of a solution of (0.1) asymptotic to x(t) = at + b, a, b &isin<br>R has been obtained. In this thesis we investigate in a systematic way the asymptotic behavior as t &rarr<br>&infin<br>of solutions of a class of differential equations of the form (p(t)x&prime<br>)&pr
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34

Johnson, M. E. "Bifurcations in lattice dynamical systems." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.605623.

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In this thesis I consider bifurcations in lattice dynamical systems, primarily coupled map lattices and lattice differential equations. First I explain how certain coupled map lattices can be considered as cellular automata, on all or part of each of state- or parameter-space, and outline what can be gained from such a consideration. Then I consider bifurcations of fixed points in locally bistable coupled map lattices, introducing various analytical techniques for the study of piecewise-linear lattice dynamical systems, and showing how numerical techniques allow smooth systems to be investigat
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35

Bernhard, Michael A. "Introduction to chaotic dynamical systems." Thesis, Monterey, California. Naval Postgraduate School, 1992. http://hdl.handle.net/10945/23708.

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Abstract (sommario):
The emerging discipline known as "chaos theory" is a relatively new field of study with a diverse range of applications (economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to gen- eral dynamical systems. Various approaches range from topological methods of a qualitative description, to physical notions of randomness, information, and entropy in crgodic theory, to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current defi
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36

Clewlow, Les. "Cellular automata and dynamical systems." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/4233/.

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In this thesis we investigate the theoretical nature of the mathematical structures termed cellular automata. Chapter 1: Reviews the origin and history of cellular automata in order to place the current work into context. Chapter 2: Develops a cellular automata framework which contains the main aspects of cellular automata structure which have appeared in the literature. We present a scheme for specifying the cellular automata rules for this general model and present six examples of cellular automata within the model. Chapter 3: Here we develop a statistical mechanical model of cellular automa
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37

Garira, Winston. "Synchronisation of coupled dynamical systems." Thesis, University of London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.399495.

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38

Bandtlow, Oscar F. "Spectral analysis of dynamical systems." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396095.

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39

Campanella, Giammarco. "Dynamical aspects of exoplanetary systems." Thesis, Queen Mary, University of London, 2013. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8374.

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The detection of more than 130 multiple planet systems makes it necessary to interpret a broader range of properties than are shown by our Solar system. This thesis covers aspects linked to the proliferation in recent years of multiple extrasolar planet systems. A narrow observational window, only partially covering the longest orbital period, can lead to solutions representing unrealistic scenarios. The best-fit solution for the three-planet extrasolar system of HD 181433 describes a highly unstable configuration. Taking into account the dynamical stability as an additional observable while i
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40

Joyner, Sheldon T. "On non-archimedean dynamical systems." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51861.

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Thesis (MSc) -- University of Stellenbosch, 2000.<br>ENGLISH ABSTRACT: A discrete dynamical system is a pair (X, cf;) comprising a non-empty set X and a map cf; : X ---+ X. A study is made of the effect of repeated application of cf; on X, whereby points and subsets of X are classified according to their behaviour under iteration. These subsets include the JULIA and FATOU sets of the map and the sets of periodic and preperiodic points, and many interesting questions arise in the study of their properties. Such questions have been extensively studied in the case of complex dynamics, but m
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41

Frisk, Martin. "Synchronization in chaotic dynamical systems." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-287624.

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42

Liu, Zheng. "Dynamical systems and random perturbations." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186232.

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This dissertation consists of two independent parts. In the first part we study the ergodic theory of surface endomorphisms. We consider non-uniformly expanding maps with generic singularities, and prove that the Pesin formula holds, which is to say that entropy is equal to the sum of the positive Lyapunov exponents if and only if the invariant probability measure in question is absolutely continuous with respect to Lebesgue measure. In the second part we study the small random perturbations of the Feigenbaum map related to the fixed point of Feigenbaum's renormalization operator for unimodal
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43

Carracedo, Rodriguez Andrea. "Approximation of Parametric Dynamical Systems." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99895.

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Abstract (sommario):
Dynamical systems are widely used to model physical phenomena and, in many cases, these physical phenomena are parameter dependent. In this thesis we investigate three prominent problems related to the simulation of parametric dynamical systems and develop the analysis and computational framework to solve each of them. In many cases we have access to data resulting from simulations of a parametric dynamical system for which an explicit description may not be available. We introduce the parametric AAA (p-AAA) algorithm that builds a rational approximation of the underlying parametric dynamical
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44

Grimm, Alexander Rudolf. "Taming of Complex Dynamical Systems." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/24775.

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Abstract (sommario):
The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D Navier-Stokes equation have global unique solutions and this open problem is one of the Millennium Prize Problems. However, many of these mathematical models are extremely useful in the understanding of complex physical systems. For years people have considered met
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45

Mcnitt, Joseph Andrew. "Stability in Graph Dynamical Systems." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83604.

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The underlying mathematical model of many simulation models is graph dynamical systems (GDS). This dynamical system, its implementation, and analyses on each will be the focus of this paper. When using a simulation model to answer a research question, it is important to describe this underlying mathematical model in which we are operating for verification and validation. In this paper we discuss analyses commonly used in simulation models. These include sensitivity analyses and uncertainty quantification, which provide motivation for stability and structure-to-function research in GDS. We revi
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46

Polo, Fabrizio. "Equidistribution on Chaotic Dynamical Systems." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306527005.

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47

Bhagavatula, Ravi S. "Topics in extended dynamical systems /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487856076416283.

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48

Kupsa, Michal. "Return times in dynamical systems." Toulon, 2005. http://www.theses.fr/2005TOUL0009.

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Dans cette thèse, deux aspects asymptotiques des temps de retour et d'entrée sont étudiés: les taux locaux de temps de retour, et les lois limites des k-ièmes temps de retour et d'entrée. Dans le cadre des "shifts" Sturmiens, des formules permettant de calculer les taux locaux de temps de retour sont développées. La classe des lois limites de premier temps d'entrée est décrite explicitement. Nous y prouvons que la classe des lois limites des k-ièmes temps de retour est la même que celle des premiers temps de retour, caractérisée par Y. Lacroix. Enfin, nous y exhibons un lien entre les lois lim
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Stergiopoulou, Aikaterini. "Dynamical Stability of Planetary Systems." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-323006.

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The study of dynamical stability in planetary systems has become possible during the last few decades due to the development of numerical methods for long-term integrations of N-body systems. Since the 90’s the number of exoplanet detections has been increased significantly, making the simulations of other real planetary systems besides the Solar System feasible. One of the exciting new-found worlds is the system Kepler-11. Six planets which are located very close to each other orbit a solar-type star. In this project we first investigate the behavior of Kepler-11 when we change some of the in
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Dundar, Veli Ufuktepe Ünal. "Dynamical Systems on Time Scales/." [s.l.]: [s.n.], 2007. http://library.iyte.edu.tr/tezler/master/matematik/T000648.pdf.

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