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Literatura académica sobre el tema "Systeme dynamiques hyperboliques"
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Tesis sobre el tema "Systeme dynamiques hyperboliques"
Leclerc, Gaétan. "Nonlinearity, fractals, Fourier decay - harmonic analysis of equilibrium states for hyperbolic dynamical systems". Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS264.
Texto completoThis PhD lies at the intersection between fractal geometry and hyperbolic dynamics. Being given a (low dimensional) hyperbolic dynamical system in some euclidean space, let us consider a fractal compact invariant subset, and an invariant probability measure supported on this fractal set with good statistical properties, such as the measure of maximal entropy. The question is the following: does the Fourier transform of the measure exhibit power decay ? Our main goal is to give evidence, for several families of hyperbolic dynamical systems, that nonlinearity of the dynamics is enough to prove such decay results. These statements will be obtained using a powerful tool from the field of additive combinatorics: the sum-product phenomenon
Gossart, Luc. "Opérateurs de transfert de systèmes dynamiques partiellement hyperboliques aléatoires". Thesis, Université Grenoble Alpes, 2020. http://www.theses.fr/2020GRALM062.
Texto completoIn this thesis, we are interested in transfer operators associated with circle extensions of hyperbolic maps. We show a convergence in law of the flat traces of the reduced transfer operators, up to an Ehrenfest time, when the roof function is random
Lamare, Pierre-Olivier. "Contrôle de systèmes hyperboliques par analyse Lyapunov". Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM062/document.
Texto completoIn this thesis we have considered different aspects for the control of hyperbolic systems.First, we have studied switched hyperbolic systems. They contain an interaction between a continuous and a discrete dynamics. Thus, the continuous dynamics may evolve in different modes: these modes are imposed by the discrete dynamics. The change in the mode may be controlled (in case of a closed-loop system), or may be uncontrolled (in case of an open-loop system). We have focused our interest on the former case. We procedeed with a Lyapunov analysis, and construct three switching rules. We have shown how to modify them to get robustness and ISS properties. We have shown their effectiveness with numerical tests.Then, we have considered the trajectory generation problem for 2x2 linear hyperbolic systems. We have solved it with backstepping. Then, we have considered the tracking problem with a Proportionnal-Integral controller. We have shown that it stabilizes the error system around the reference trajectory with a new non-diagonal Lyapunov function. The integral action has been shown to be able to reject in-domain, as well as boundary disturbances.Finally, we have considered numerical aspects for the Lyapunov analysis. The conditions for the stability and design of controllers by quadratic Lyapunov functions involve an infinity of matrix inequalities. We have shown how to reduce this complexity by polytopic embeddings of the constraints.Many obtained results have been illustrated by academic examples and physically relevant dynamical systems (as Shallow-Water equations and Aw-Rascle-Zhang equations)
Coudène, Yves. "Ergodicite du feuilletage stable des flots hyperboliques definis sur un revetement abelien". Palaiseau, Ecole polytechnique, 2000. http://www.theses.fr/2000EPXX0014.
Texto completoBouloc, Damien. "Géométrie et topologie de systèmes dynamiques intégrables". Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30099/document.
Texto completoIn this thesis, we are interested in two different aspects of integrable dynamical systems. The first part is devoted to the study of three families of integrable Hamiltonian systems: the systems of bending flows of Kapovich and Millson on the moduli spaces of 3D polygons with fixed side lengths, the Gelfand-Cetlin systems introduced by Guillemin and Sternberg on the coadjoint orbits of the Lie group U(n), and a family of integrable systems defined by Nohara and Ueda on the Grassmannian Gr(2,n). In each case we prove that the fibers of the momentum map are embedded submanifolds for which we give geometric models in terms of quotients manifolds. In the second part we carry on with a study initiated by Zung and Minh of the totally hyperbolic actions of R^n on compact n-dimensional manifolds that appear naturally when investigating integrable non-hamiltonian systems with nondegenerate singularities. We study the flow generated by the action of a generic vector in Rn. We define a notion of index for its singularities and we use this flow to obtain results on the number of orbits of given dimension. We investigate further the 2-dimensional case, and more particularly the case of the sphere S2, where the orbits of the action draw an embedded graph of which we analyse the combinatorics. Finally, we provide explicit examples of totally hyperbolic actions in dimension 3, on the sphere S3 and on the projective space RP3
Reygner, Julien. "Comportements en temps long et à grande échelle de quelques dynamiques de collision". Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066471/document.
Texto completoThis thesis contains three independent parts, each one of which is dedicated to the study of a particle system, following either a deterministic or a stochastic dynamics, and in which interactions only occur at collisions. Part I contains a numerical and theoretical study of nonequilibrium steady states of the Complete Exchange Model, which was introduced by physicists in order to understand heat transfer in some porous materials. Part II is dedicated to a system of Brownian particles evolving on the real line and interacting through their ranks. The long time and mean-field behaviour of this system is described, then the results are applied to the study of a model of equity market called the mean-field Atlas model. Part III introduces a multitype version of the particle system studied in the previous part, which allows to approximate parabolic systems of nonlinear partial differential equations. The small noise limit of of this system is called multitype sticky particle dynamics and now approximates hyperbolic systems. A detailed study of this dynamics provides stability estimates in Wasserstein distance for the solutions of these systems
Le, Ba Khiet. "Stabilité des systèmes dynamiques non-réguliers et applications". Limoges, 2013. http://www.theses.fr/2013LIMO4054.
Texto completoThis manuscript deals with the stability of non-smooth dynamical systems and applications. More precisely, we aim to provide a formulation to study the stability analysis of non-smooth dynamical systems, particularly in electrical circuits and mechanics with dry friction and robustness. The efficient tools which we have used are non-smooth analysis, Lyapunov stability theorem and non-smooth mathematical frameworks : complementarity and differentials inclusions. In details, we use complementarity formalism to model some simple switch systems and differential inclusions to model a Dc-Dc Buck converter, Lagrange dynamical systems and Lur'e systems. For each model, we are interested in the well-posedness, stability properties of trajectories, even finite-time stability or putting a control force to obtain finite-time stability, and finding numerical ways to simulate the systems. The theoretical results are supported by some examples in electrical circuits and mechanics with numerical simulations. It is noted that the method used in this monograph can be applied to analyze for non-smooth dynamical systems from other fields such as economics, finance or biology. .
Monson, Björn. "Pavages de la droite réelle, du demi-plan hyperbolique et automorphismes du groupe libre". Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4060/document.
Texto completoIn this thesis, we construct tilings of the real line and the hyperbolic half-plane using train-track maps of IWIP free group automorphisms. One the one hand, we use a substitution defined by P. Arnoux, V. Berthé, A. Siegel, A. Hilion coming from a train-track map of a IWIP free group automorphism to generate substitutive aperiodic tilings of the real line. We show, thanks to a theorem of J. Los about connectivity of train-track representatives of an IWIP automorphism, that the topological type of those tiling spaces is the same up to a choice of train-track representative. Thus we associate, up to an homeomorphism, a tiling space of the real line to a class of an IWIP outer automorphism of Fn, then we extend this result to a conjugacy class of an IWIP element in Out(Fn). On the other hand, we construct from elements of tiling spaces of the real line previously defined, a set of weakly aperiodic for the affine group tilings of the hyperbolic half-plane. We study topological et dynamical properties of the tiling space generated by those hyperbolic tilings. Finally, in the last section we endow tiling spaces previously constructed with a smooth structure thanks to their inverse limit structure
Villedieu, Philippe. "Approximations de type cinétique du système hyperbolique de la dynamique des gaz hors équilibre thermochimique". Toulouse 3, 1994. http://www.theses.fr/1994TOU30276.
Texto completoDutilleul, Tom. "Dynamique chaotique des espaces-temps spatialement homogènes". Thesis, Paris 13, 2019. http://www.theses.fr/2019PA131019.
Texto completoIn 1963, Belinsky, Khalatnikov and Lifshitz have proposed a conjectural description of the asymptotic geometry of cosmological models in the vicinity of their initial singularity. In particular, it is believed that the asymptotic geometry of generic spatially homogeneous spacetimes should display an oscillatory chaotic behaviour modeled on a discrete map’s dynamics (the so-called Kasner map). We prove that this conjecture holds true, if not for generic spacetimes, at least for a positive Lebesgue measure set of spacetimes. In the context of spatially homogeneous spacetimes, the Einstein field equations can be reduced to a system of differential equations on a finite dimensional phase space: the Wainwright-Hsu equations. The dynamics of these equations encodes the evolution of the geometry of spacelike slices in spatially homogeneous spacetimes. Our proof is based on the non-uniform hyperbolicity of the Wainwright-Hsu equations. Indeed, we consider the return map of the solutions of these equations on a transverse section and prove that it is a non-uniformly hyperbolic map with singularities. This allows us to construct some local stable manifolds à la Pesin for this map and to prove that the union of the orbits starting in these local stable manifolds cover a positive Lebesgue measure set in the phase space. The chaotic oscillatory behaviour of the corresponding spacetimes follows. The Wainwright-Hsu equations turn out to be quite interesting and challenging from a purely dynamical system viewpoint. In order to understand the asymptotic behaviour of (many of) the solutions of these equations, we will in particular be led to: • carry a detailed analysis of the local dynamics of a vector field in the neighborhood of degenerate nonlinearizable partially hyperbolic singularities, • deal with non-uniformly hyperbolic maps with singularities for which the usual theory (due to Pesin and Katok-Strelcyn) is not relevant due to the poor regularity of the maps, • consider some unusual arithmetic conditions expressed in terms of continued fractions and use some rather sophisticated ergodic properties of the Gauss map to prove that these properties are generic
Libros sobre el tema "Systeme dynamiques hyperboliques"
V, Anosov D., ed. Dynamical systems with hyperbolic behavior. Berlin: Springer-Verlag, 1995.
Buscar texto completoCoornaert, M. Symbolic dynamcis [i.e. dynamics] and hyperbolic groups. Berlin: Springer-Verlag, 1993.
Buscar texto completoCapítulos de libros sobre el tema "Systeme dynamiques hyperboliques"
"V. Dynamique hyperbolique II". En Théorie des systèmes dynamiques, 109–48. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-1050-5-006.
Texto completo"IV. Dynamique hyperbolique I". En Théorie des systèmes dynamiques, 85–108. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-1050-5-005.
Texto completo"V. Dynamique hyperbolique II". En Théorie des systèmes dynamiques, 109–48. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-1050-5.c006.
Texto completo"IV. Dynamique hyperbolique I". En Théorie des systèmes dynamiques, 85–108. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-1050-5.c005.
Texto completo"3 ÉTUDE LOCALE DES SINGULARITÉS HYPERBOLIQUES". En Des équations différentielles aux systèmes dynamiques II, 59–110. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-1215-8-004.
Texto completo"3 ÉTUDE LOCALE DES SINGULARITÉS HYPERBOLIQUES". En Des équations différentielles aux systèmes dynamiques II, 59–110. EDP Sciences, 2020. http://dx.doi.org/10.1051/978-2-7598-1215-8.c004.
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