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Regularity of invariant graphs over hyperbolic systems

Hadjiloukas, D., Nicol, Matthew and Walkden, C. (2002) Regularity of invariant graphs over hyperbolic systems Dynamical Systems, 22. pp. 469-482.


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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
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Hadjiloukas, D.
Nicol, Matthew
Walkden, C.
Date : 1 April 2002
Additional Information : Published in Ergodic Theory and Dynamical Systems, 22, 469-482. © 2002 Cambridge University Press. Reprinted with permission.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 31 Oct 2017 14:02

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