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Regularity of invariant graphs over hyperbolic systems

Published online by Cambridge University Press:  07 May 2002

D. HADJILOUCAS ,
M. J. NICOL  and
C. P. WALKDEN
D. HADJILOUCAS
Affiliation:
Department of Mathematics, UMIST, Manchester M60 1QD, UK (e-mail: [email protected])
M. J. NICOL
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK (e-mail: [email protected])
C. P. WALKDEN
Affiliation:
Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, UK (e-mail: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 2 , April 2002 , pp. 469 - 482
Copyright
2002 Cambridge University Press

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