Boundedness and invariant metrics for diffeomorphism cocycles over hyperbolic systems

Research output: Contribution to journalArticle

Abstract

Let A be a Hölder continuous cocycle over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold M. We consider the periodic data of A, i.e., the set of its return values along the periodic orbits in the base. We show that if the periodic data of A is bounded in Diffq(M), q> 1 , then the set of values of the cocycle is bounded in Diffr(M) for each r< q. Moreover, such a cocycle is isometric with respect to a Hölder continuous family of Riemannian metrics on M.

Original languageEnglish (US)
Pages (from-to)401-417
Number of pages17
JournalGeometriae Dedicata
Volume202
Issue number1
DOIs
StatePublished - Oct 1 2019

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Invariant Metric
Diffeomorphism
Cocycle
Hyperbolic Systems
Boundedness
Group of Diffeomorphisms
Riemannian Metric
Isometric
Compact Manifold
Periodic Orbits
Dynamical system

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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Boundedness and invariant metrics for diffeomorphism cocycles over hyperbolic systems. / Sadovskaya, Victoria V.

In: Geometriae Dedicata, Vol. 202, No. 1, 01.10.2019, p. 401-417.

Research output: Contribution to journalArticle

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