Regularity of invariant graphs over hyperbolic systems

Hadjiloucas, D. and Nicol, M. J. and Walkden, C. P. (2002) Regularity of invariant graphs over hyperbolic systems. Ergodic Theory and Dynamical Systems, 22 (2). pp. 469-482. ISSN 0143-3857

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Abstract

We consider cocycles with negative Lyapunov exponents defined over a hyperbolic dynamical system. It is well known that such systems possess invariant graphs and that under spectral assumptions these graphs have some degree of Hölder regularity. When the invariant graph has a slightly higher Hölder exponent than the a priori lower bound on an open set (even on just a set of positive measure for certain systems), we show that the graph must be Lipschitz or (in the Anosov case) as smooth as the cocycle.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User:	Ms Lucy van Russelt
Date Deposited:	16 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/521

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