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Cohomology of fiber-bunched twisted cocycles over hyperbolic systems

Part of: Ergodic theory Dynamical systems with hyperbolic behavior Random dynamical systems

Published online by Cambridge University Press:  21 July 2020

Lucas Backes
Lucas Backes*
Affiliation:
Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre, Rio Grande do Sul, Brazil ([email protected])
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Abstract

A twisted cocycle taking values on a Lie group G is a cocycle that is twisted by an automorphism of G in each step. In the case where G = GL(d, ℝ), we prove that if two Hölder continuous twisted cocycles satisfying the so-called fiber-bunching condition have the same periodic data then they are cohomologous.

Keywords

twisted cocyclescohomologyhyperbolic systemsperiodic points

MSC classification

Primary: 37H05: Foundations, general theory of cocycles, algebraic ergodic theory 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Secondary: 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 3 , August 2020 , pp. 844 - 860
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Copyright
Copyright © The Authors, 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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