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Academic literature on the topic 'Cocycles'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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Journal articles on the topic "Cocycles"

1

SADOVSKAYA, VICTORIA. "Cohomology of fiber bunched cocycles over hyperbolic systems." Ergodic Theory and Dynamical Systems 35, no. 8 (August 4, 2014): 2669–88. http://dx.doi.org/10.1017/etds.2014.43.

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We consider Hölder continuous fiber bunched $\text{GL}(d,\mathbb{R})$-valued cocycles over an Anosov diffeomorphism. We show that two such cocycles are Hölder continuously cohomologous if they have equal periodic data, and prove a result for cocycles with conjugate periodic data. We obtain a corollary for cohomology between any constant cocycle and its small perturbation. The fiber bunching condition means that non-conformality of the cocycle is dominated by the expansion and contraction in the base. We show that this condition can be established based on the periodic data. Some important examples of cocycles come from the differential of a diffeomorphism and its restrictions to invariant sub-bundles. We discuss an application of our results to the question of whether an Anosov diffeomorphism is smoothly conjugate to a $C^{1}$-small perturbation. We also establish Hölder continuity of a measurable conjugacy between a fiber bunched cocycle and a uniformly quasiconformal one. Our main results also hold for cocycles with values in a closed subgroup of $\text{GL}(d,\mathbb{R})$, for cocycles over hyperbolic sets and shifts of finite type, and for linear cocycles on a non-trivial vector bundle.

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DAMJANOVIĆ, DANIJELA, and DISHENG XU. "Diffeomorphism group valued cocycles over higher-rank abelian Anosov actions." Ergodic Theory and Dynamical Systems 40, no. 1 (April 5, 2018): 117–41. http://dx.doi.org/10.1017/etds.2018.22.

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We prove that every smooth diffeomorphism group valued cocycle over certain$\mathbb{Z}^{k}$Anosov actions on tori (and more generally on infranilmanifolds) is a smooth coboundary on a finite cover, if the cocycle is center bunched and trivial at a fixed point. For smooth cocycles which are not trivial at a fixed point, we have smooth reduction of cocycles to constant ones, when lifted to the universal cover. These results on cocycle trivialization apply, via the existing global rigidity results, to maximal Cartan$\mathbb{Z}^{k}$($k\geq 3$) actions by Anosov diffeomorphisms (with at least one transitive), on any compact smooth manifold. This is the first rigidity result for cocycles over$\mathbb{Z}^{k}$actions with values in diffeomorphism groups which does not require any restrictions on the smallness of the cocycle or on the diffeomorphism group.

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FARMER, D. G., and K. J. HORADAM. "A POLYNOMIAL APPROACH TO COCYCLES OVER ELEMENTARY ABELIAN GROUPS." Journal of the Australian Mathematical Society 85, no. 2 (October 2008): 177–90. http://dx.doi.org/10.1017/s1446788708000876.

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AbstractWe derive bivariate polynomial formulae for cocycles and coboundaries in Z2(ℤpn,ℤpn), and a basis for the (pn−1−n)-dimensional GF(pn)-space of coboundaries. When p=2 we determine a basis for the $(2^n + {n\choose 2} -1)$-dimensional GF(2n)-space of cocycles and show that each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form.

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Manuilov, Vladimir, and Chao You. "Vector bundles from generalized pairs of cocycles." International Journal of Mathematics 25, no. 06 (June 2014): 1450061. http://dx.doi.org/10.1142/s0129167x1450061x.

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It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still determine vector bundles.

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LINDSAY, J. MARTIN, and STEPHEN J. WILLS. "Quantum stochastic operator cocycles via associated semigroups." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 3 (May 2007): 535–56. http://dx.doi.org/10.1017/s0305004106009923.

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AbstractA recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their stochastic generators. This leads to new existence results for quantum stochastic differential equations. We also give necessary and sufficient conditions for a cocycle to satisfy such an equation.

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KARAKHANYAN, D. R., R. P. MANVELYAN, and R. L. MKRTCHYAN. "TRACE ANOMALIES AND COCYCLES OF WEYL AND DIFFEOMORPHISMS GROUPS." Modern Physics Letters A 11, no. 05 (February 20, 1996): 409–21. http://dx.doi.org/10.1142/s021773239600045x.

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The general structure of trace anomaly, suggested recently by Deser and Schwimmer is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the cocycles of the Weyl group in d=2k dimensions is considered, and explicit answers for d=4, 6 are obtained. In particular, it is shown that addition of the special combination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field σ, i.e. the form, similar to the two-dimensional Liouville action. This form also establishes the connection of the cocycles with conformal-invariant operators of order d and zero weight. We also give the general rule for transformation of that cocycles into the cocycles of diffeomorphisms group.

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Mortier, Arnaud. "Finite-type 1-cocycles of knots given by Polyak–Viro Formulas." Journal of Knot Theory and Its Ramifications 24, no. 10 (September 2015): 1540004. http://dx.doi.org/10.1142/s0218216515400040.

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We present a new method to produce simple formulas for 1-cocycles of knots over the integers, inspired by Polyak–Viro's formulas for finite-type knot invariants. We conjecture that these 1-cocycles represent finite-type cohomology classes in the sense of Vassiliev. An example of degree 3 is studied, and shown to coincide over ℤ2 with the Teiblum–Turchin cocycle [Formula: see text].

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Clark, W. Edwin, Larry A. Dunning, and Masahico Saito. "Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles." Journal of Knot Theory and Its Ramifications 26, no. 07 (February 24, 2017): 1750035. http://dx.doi.org/10.1142/s0218216517500353.

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We explore a knot invariant derived from colorings of corresponding [Formula: see text]-tangles with arbitrary connected quandles. When the quandle is an abelian extension of a certain type the invariant is equivalent to the quandle [Formula: see text]-cocycle invariant. We construct many such abelian extensions using generalized Alexander quandles without explicitly finding [Formula: see text]-cocycles. This permits the construction of many [Formula: see text]-cocycle invariants without exhibiting explicit [Formula: see text]-cocycles. We show that for connected generalized Alexander quandles the invariant is equivalent to Eisermann’s knot coloring polynomial. Computations using this technique show that the [Formula: see text]-cocycle invariant distinguishes all of the oriented prime knots up to 11 crossings and most oriented prime knots with 12 crossings including classification by symmetry: mirror images, reversals, and reversed mirrors.

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BOCKER-NETO, CARLOS, and MARCELO VIANA. "Continuity of Lyapunov exponents for random two-dimensional matrices." Ergodic Theory and Dynamical Systems 37, no. 5 (March 8, 2016): 1413–42. http://dx.doi.org/10.1017/etds.2015.116.

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KATOK, ANATOLE, VIOREL NIŢICĂ, and ANDREI TÖRÖK. "Non-abelian cohomology of abelian Anosov actions." Ergodic Theory and Dynamical Systems 20, no. 1 (February 2000): 259–88. http://dx.doi.org/10.1017/s0143385700000122.

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We develop a new technique for calculating the first cohomology of certain classes of actions of higher-rank abelian groups (${\mathbb Z}^k$ and ${\mathbb R}^k$, $k\ge 2$) with values in a linear Lie group. In this paper we consider the discrete-time case. Our results apply to cocycles of different regularity, from Hölder to smooth and real-analytic. The main conclusion is that the corresponding cohomology trivializes, i.e. that any cocycle from a given class is cohomologous to a constant cocycle. The principal novel feature of our method is its geometric character; no global information about the action based on harmonic analysis is used. The method can be developed to apply to cocycles with values in certain infinite dimensional groups and to rigidity problems.

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Dissertations / Theses on the topic "Cocycles"

1

Skalski, Adam G. "Quantum stochastic convolution cocycles." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.438288.

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at, Klaus Schmidt@univie ac. "Invariant Cocycles have Abelian Ranges." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi935.ps.

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Spelling, James Allan. "Comparison of two metaplectic cocycles." Thesis, University College London (University of London), 2004. http://discovery.ucl.ac.uk/1383231/.

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In my thesis I shall be investigating two distinct metaplectic extensions of the general linear group. The first of these was discovered by Matsumoto, it's existence intimately connected with the deep properties of the r-th order Hilbert symbol. His construction relies heavily on class field theory and algebraic K-theory. Having constructed his metaplectic group, which is known to be universal, Matsumoto was then able to define the cocycle representing this extension. The second of these metaplectic extensions was found recently by Dr Hill at University College London. In contrast, his construction is very elementary. He was able to prove the existence of a continuous cocycle resulting in the construction of a new non-trivial metaplectic extension. It has already been shown, by Hill, that these two metaplectic extensions are isomorphic if we restrict to the special linear group. However, little is known of this isomorphism. Throughout this thesis we shall investigate these two cocycles, finding explicit formulae in both cases. We shall then show that the isomorphism between the group extensions of Matsumoto and Hill may be defined via the discovery of the coboundary which splits the quotient of the corresponding cocycles. Having found this coboundary we shall then be able to prove that, in specific cases, the two extensions are in fact isomorphic over the full general linear group.

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Bradshaw, W. S. "Quantum diffusions and stochastic cocycles." Thesis, University of Nottingham, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329848.

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Chavaudret, Claire. "Réductibilité des cocycles quasi-périodiques." Paris 7, 2010. http://www.theses.fr/2010PA077010.

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Cette thèse est consacrée à la réductibilité et à la presque-réductibilité des cocycles quasi-périodiques, qui sont les solutions fondamentales de systèmes différentiels linéaires à coefficients quasi-périodiques. On introduit une notion de conjugaison, au sens des cocycles, par une transformation quasi-périodique; les quantités invariantes par ce type de conjugaison sont appelés invariants dynamiques. Le caractère réductible d'un cocycle permet de connaître très bien ses invariants dynamiques, tels que les exposants de Lyapunov qui indiquent le comprtement asymptotique des solutions du système, et en dimension 2, le nombre de rotation qui donne leur rotation moyenne autour de l'origine. La presque réductibilité permet de connaître assez bien ces invariants sur un temps arbitrairement long. On définit la réductibilité d' un cocycle dans un groupe de Lie linéaire G modulo 1 ou 2 comme étant la possibilité de réduire ce cocycle par une transformation à valeurs dans G et définie soit sur le tore, soit sur un revêtement du tore; on montre par une méthode géométrique qu' un cocycle réductible dans le groupe des matrices inversibles et à valeurs dans G est réductible dans G modulo 1 si G est complexe et modulo 2 si G est réel. La deuxième partie porte sur la notion de presque réductibilité, c1 est-à-dire la possibilité de conjuguer un cocycle à un autre qui est arbitrairement proche d' un cocycle réductible, dans une topologie fixée. On démontre un résultat perturbatif de presque-réductibilité des cocycles analytiques à fréquence diophantienne proches d' un cocycle constant et qui sont à valeurs dans le groupe sympleçtique. La presque-réductibilité est obtenue dans F espace des fonctions analytiques sur un voisinage fixe du tore. Avec un seul doublement de période, par une méthode de type KAM quantifiant la fréquence de F apparition de petits diviseurs, ou résonances. Un corollaire en est la quasi-densité, dans cette topologie, des cocycles réductibles au voisinage d' un cocycle constant
This thesis is dedicated to the study of reducibility and almost reducibility of quasi-periodic cocycles, which are the fundamental solutions of linear differential Systems with quasi-periodic coefficients. A notion of conjugation, in the sense of cocycles, by a quasi-periodic transformation, is introduced; quantities which are invariant by this type of conjugation are called dynamical invariants. When a cocycle is reducible, it is possible to have a good knowledge of its dynamical invariants, such as Lyapunov exponents which indicate the asymptotic behaviour of the solutions of the System, and in dimension 2, the rotation number which gives their mean rotation around the origin. Almost reducibility enables one to have quite a good control on these invariants on an arbitrarily long time. One introduces the notion of reducibility of a cocycle in a linear Lie group G modulo 1 or 2, as the possibility of reducing the cocycle by means of a transformation with values in G and which is defined either on the torus, or on a covering of the torus; it is then shown by a geometric argument that a cocycle with values in G which is reducible in the group of invertible matrices is reducible in G modulo 1 if G is complex and modulo 2 if G is real. The second part concerns the problem of almost reducibility, that is, whether it is possible to conjugate a cocycle to another one which is arbitrarily close to a reducible cocycle, in some fixed topology. We state and prove a perturbative result of almost reducibility of analytic cocycles with diophantine frequency which are close to a constant cocycle and take their values in the symplectic group. Almost reducibility is obtained in the space of analytic functions on a fixed neighbourhood of the torus, with only one period doubling, through a KAM-type method estimating how often small divisors, or resonances, appear. Quasi-density in this topology of reducible cocycles near a constant comes as a corollary

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Sarti, Filippo <1993&gt. "Numerical invariants for measurable cocycles." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amsdottorato.unibo.it/10160/2/tesi.pdf.

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The theory of numerical invariants for representations can be generalized to measurable cocycles. This provides a natural notion of maximality for cocycles associated to complex hyperbolic lattices with values in groups of Hermitian type. Among maximal cocycles, the class of Zariski dense ones turns out to have a rigid behavior. An alternative implementation of numerical invariants can be given by using equivariant maps at the level of boundaries and by exploiting the Burger-Monod approach to bounded cohomology. Due to their crucial role in this theory, we prove existence results in two different contexts. Precisely, we construct boundary maps for non-elementary cocycles into the isometry group of CAT(0)-spaces of finite telescopic dimension and for Zariski dense cocycles into simple Lie groups. Then we approach numerical invariants. Our first goal is to study cocycles from complex hyperbolic lattices into the Hermitian group SU(p,q). Following the theory recently developed by Moraschini and Savini, we define the Toledo invariant by using the pullback along cocycles, also by involving boundary maps. For cocycles Γ × X → SU(p,q) with 1

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Kaimanovich, Vadim, Klaus Schmidt, and Klaus Schmidt@univie ac at. "Ergodicity of cocycles. 1: General Theory." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi936.ps.

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8

Demircioglu, Aydin. "Reconstruction of deligne classes and cocycles." Phd thesis, Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2007/1375/.

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In der vorliegenden Arbeit verallgemeinern wir im Wesentlichen zwei Theoreme von Mackaay-Picken und Picken (2002, 2004). Im ihrem Artikel zeigen Mackaay und Picken,dass es eine bijektive Korrespodenz zwischen Deligne 2-Klassen $xi in check{H}^2(M, mathcal{D}^2)$ und Holonomie Abbildungen von der zweiten dünnen Homotopiegruppe $pi_2^2(M)$ in die abelsche Gruppe $U(1)$ gibt. Im zweiten Artikel wird eine Verallgemeinerung dieses Theorems bewiesen: Picken zeigt, dass es eine Bijektion gibt zwischen Deligne 2-Kozykeln und gewissen 2-dimensionalen topologischen Quantenfeldtheorien. In dieser Arbeit zeigen wir, dass diese beiden Theoreme in allen Dimensionen gelten.Wir betrachten zunächst den Holonomie Fall und können mittels simplizialen Methoden nachweisen, dass die Gruppe der glatten Deligne $d$-Klassen isomorph ist zu der Gruppe der glatten Holonomie Abbildungen von der $d$-ten dünnen Homotopiegruppe $pi_d^d(M)$ nach $U(1)$, sofern $M$ eine $(d-1)$-zusammenhängende Mannigfaltigkeit ist. Wir vergleichen dieses Resultat mit einem Satz von Gajer (1999). Gajer zeigte, dass jede Deligne $d$-Klasse durch eine andere Klasse von Holonomie-Abbildungen rekonstruiert werden kann, die aber nicht nur Holonomien entlang von Sphären, sondern auch entlang von allgemeinen $d$-Mannigfaltigkeiten in $M$ enthält. Dieser Zugang benötigt dann aber nicht, dass $M$ hoch-zusammenhängend ist. Wir zeigen, dass im Falle von flachen Deligne $d$-Klassen unser Rekonstruktionstheorem sich von Gajers unterscheidet, sofern $M$ nicht als $(d-1)$, sondern nur als $(d-2)$-zusammenhängend angenommen wird. Stiefel Mannigfaltigkeiten besitzen genau diese Eigenschaft, und wendet man unser Theorem auf diese an und vergleicht das Resultat mit dem von Gajer, so zeigt sich, dass es zuviele Deligne Klassen rekonstruiert. Dies bedeutet, dass unser Rekonstruktionsthreorem ohne die Zusatzbedingungen an die Mannigfaltigkeit M nicht auskommt, d.h. unsere Rekonstruktion benötigt zwar weniger Informationen über die Holonomie entlang von d-dimensionalen Mannigfaltigkeiten, aber dafür muss M auch $(d-1)$-zusammenhängend angenommen werden. Wir zeigen dann, dass auch das zweite Theorem verallgemeinert werden kann: Indem wir das Konzept einer Picken topologischen Quantenfeldtheorie in beliebigen Dimensionen einführen, können wir nachweisen, dass jeder Deligne $d$-Kozykel eine solche $d$-dimensionale Feldtheorie mit zwei besonderen Eigenschaften, der dünnen Invarianz und der Glattheit, induziert. Wir beweisen, dass jede $d$-dimensionale topologische Quantenfeldtheorie nach Picken mit diesen zwei Eigenschaften auch eine Deligne $d$-Klasse definiert und prüfen nach, dass diese Konstruktion sowohl surjektiv als auch injektiv ist. Demzufolge sind beide Gruppen isomorph.
In this thesis we mainly generalize two theorems from Mackaay-Picken and Picken (2002, 2004). In the first paper, Mackaay and Picken show that there is a bijective correspondence between Deligne 2-classes $xi in check{H}^2(M,mathcal{D}^2)$ and holonomy maps from the second thin-homotopy group $pi_2^2(M)$ to $U(1)$. In the second one, a generalization of this theorem to manifolds with boundaries is given: Picken shows that there is a bijection between Deligne 2-cocycles and a certain variant of 2-dimensional topological quantum field theories. In this thesis we show that these two theorems hold in every dimension. We consider first the holonomy case, and by using simplicial methods we can prove that the group of smooth Deligne $d$-classes is isomorphic to the group of smooth holonomy maps from the $d^{th}$ thin-homotopy group $pi_d^d(M)$ to $U(1)$, if $M$ is $(d-1)$-connected. We contrast this with a result of Gajer (1999). Gajer showed that Deligne $d$-classes can be reconstructed by a different class of holonomy maps, which not only include holonomies along spheres, but also along general $d$-manifolds in $M$. This approach does not require the manifold $M$ to be $(d-1)$-connected. We show that in the case of flat Deligne $d$-classes, our result differs from Gajers, if $M$ is not $(d-1)$-connected, but only $(d-2)$-connected. Stiefel manifolds do have this property, and if one applies our theorem to these and compare the result with that of Gajers theorem, it is revealed that our theorem reconstructs too many Deligne classes. This means, that our reconstruction theorem cannot live without the extra assumption on the manifold $M$, that is our reconstruction needs less informations about the holonomy of $d$-manifolds in $M$ at the price of assuming $M$ to be $(d-1)$-connected. We continue to show, that also the second theorem can be generalized: By introducing the concept of Picken-type topological quantum field theory in arbitrary dimensions, we can show that every Deligne $d$-cocycle induces such a $d$-dimensional field theory with two special properties, namely thin-invariance and smoothness. We show that any $d$-dimensional topological quantum field theory with these two properties gives rise to a Deligne $d$-cocycle and verify that this construction is surjective and injective, that is both groups are isomorphic.

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Bates, Teresa. "Bounded cocycles: von Neumann algebras and amenability." Thesis, University of Ottawa (Canada), 1995. http://hdl.handle.net/10393/10278.

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In a 1993 preprint Guyan Robertson proved that every uniformly bounded representation of a discrete group on a finite von Neumann algebra is similar to a unitary representation. We have since discovered that this result was first proved in a paper of Vasilescu and Zsido, published in 1974 (VZ). In this thesis we generalise this result for discrete groupoids, proving that every uniformly bounded cocycle into a finite von Neumann algebra is cohomologous to a unitary cocycle. The corresponding result for cocycles into finite dimensional algebras was proved in (Zim3). We also derive some equivalent definitions of amenability of group actions and provide a new proof of a result of Zimmer regarding uniformly bounded cocycles on amenable G-spaces. We develop some machinery in order to prove these results. This is the theory of ${\cal G}$-flows in which we explore the actions of groupoids on Borel fields of sets. Our development of this theory follows that of the usual theory of flows from topological dynamics.

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Ameur, Kheira. "Polynomial quandle cocycles, their knot invariants and applications." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001813.

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Books on the topic "Cocycles"

1

Bhat, B. V. Rajarama. Cocycles of CCR flows. Providence, R.I: American Mathematical Society, 2001.

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Duarte, Pedro, and Silvius Klein. Lyapunov Exponents of Linear Cocycles. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-124-6.

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Avila, Artur. Cocycles over partially hyperbolic maps. Paris: Société mathématique de France, 2013.

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Walkden, Charles Peter. Cocycles in hyperbolic dynamics: Livsic regularity theorems and applications to stable ergodicity. [s.l.]: typescript, 1997.

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Kloeden, Peter E. Nonautonomous dynamical systems. Providence, R.I: American Mathematical Society, 2011.

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Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. Providence, Rhode Island: American Mathematical Society, 2016.

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One-Cocycles and Knot Invariants. World Scientific Publishing Co Pte Ltd, 2022.

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One-Cocycles and Knot Invariants. World Scientific Publishing Co Pte Ltd, 2022.

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Fiedler, Thomas. Polynomial One-Cocycles for Knots and Closed Braids. World Scientific Publishing Co Pte Ltd, 2019.

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Zoller, D. Cocycles, the descent equations, and the Virasoro algebra. 1990.

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Book chapters on the topic "Cocycles"

1

Jardine, John F. "Cocycles." In Springer Monographs in Mathematics, 139–57. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2300-7_6.

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Horadam, K. J., and A. A. I. Perera. "Codes from cocycles." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 151–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63163-1_12.

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Helson, Henry. "Distribution of cocycles." In The Spectral Theorem, 53–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0101633.

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Zeidler, Eberhard. "Cocycles and Observers." In Quantum Field Theory III: Gauge Theory, 871–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22421-8_17.

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Kechris, Alexander. "Cocycles and cohomology." In Mathematical Surveys and Monographs, 125–86. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/surv/160/03.

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Horadam, Kathy J. "Sequences from Cocycles." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 121–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46796-3_12.

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Barreira, Luís. "Cocycles and Lyapunov Exponents." In Lyapunov Exponents, 203–22. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71261-1_10.

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Helson, Henry. "Cocycles on the line." In The Spectral Theorem, 76–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0101634.

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Benoist, Yves, and Jean-François Quint. "Limit Laws for Cocycles." In Random Walks on Reductive Groups, 191–202. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47721-3_12.

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Aaronson, Jon. "Cocycles and skew products." In Mathematical Surveys and Monographs, 247–74. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/surv/050/08.

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Conference papers on the topic "Cocycles"

1

GOUËZEL, SÉBASTIEN. "SUBADDITIVE COCYCLES AND HOROFUNCTIONS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0124.

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2

LIEBSCHER, VOLKMAR. "ISOMETRIC COCYCLES RELATED TO BEAM SPLITTINGS." In Proceedings of the Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704290_0012.

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3

Greschonig, Gernot. "Real cocycles of point-distal minimal flows." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0540.

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4

Ivanov, Alexey V. "Exponential dichotomy of linear cocycles over irrational rotations." In 2020 Days on Diffraction (DD). IEEE, 2020. http://dx.doi.org/10.1109/dd49902.2020.9274638.

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5

BHAT, B. V. RAJARAMA, and J. MARTIN LINDSAY. "REGULAR QUANTUM STOCHASTIC COCYCLES HAVE EXPONENTIAL PRODUCT SYSTEMS." In From Foundations to Applications. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702104_0009.

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6

Ivanov, Alexey V. "Interfering circle combs and uniform hyperbolicity of cocycles." In 2023 Days on Diffraction (DD). IEEE, 2023. http://dx.doi.org/10.1109/dd58728.2023.10325785.

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7

Lindsay, J. Martin, and Adam G. Skalski. "Quantum stochastic convolution cocycles –-algebraic and C*-algebraic." In Quantum Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc73-0-24.

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8

Ivanov, Alexey V. "On linear cocycles over irrational rotations with secondary collisions." In 2021 Days on Diffraction (DD). IEEE, 2021. http://dx.doi.org/10.1109/dd52349.2021.9598487.

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9

Stoica, Diana, Mihail Megan, and Dan Ludovic Lemle. "Polynomial stability in mean square of stochastic cocycles in Hilbert spaces." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825841.

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Stoica, Codruţa. "An approach to evolution cocycles from a stochastic point of view." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0083066.

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Reports on the topic "Cocycles"

1

Neeb, Karl-Hermann. Lie Algebra Extensions and Higher Order Cocycles. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-5-2006-48-74.

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2

Jafari, Farhad, Zbigniew Slodkowski, and Thomas Tonev. Semigroups of Operators on Hardy Spaces and Cocycles of Flows. Fort Belvoir, VA: Defense Technical Information Center, April 2008. http://dx.doi.org/10.21236/ada513219.

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