Local Hölder regularity of densities and Livsic theorems for non-uniformly hyperbolic diffeomorphisms

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October 2005, 13(5): 1247-1256. doi: 10.3934/dcds.2005.13.1247

Local Hölder regularity of densities and Livsic theorems for non-uniformly hyperbolic diffeomorphisms

1.	Department of Mathematics, Warwick University, Coventry CV4 7AL, United Kingdom

Received December 2004 Revised June 2005 Published September 2005

Abstract
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We consider the partial analogue of the usual measurable Livsic theorem for Anosov diffeomorphims in the context of non-uniformly hyperbolic diffeomorphisms (Theorem 2). Our main application of this theorem is to the density of absolutely continuous measures (Theorem 1).

Keywords: Hölder function., Anosov flows, stable manifolds.

Mathematics Subject Classification: 14X.

Citation: Mark Pollicott. Local Hölder regularity of densities and Livsic theorems for non-uniformly hyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1247-1256. doi: 10.3934/dcds.2005.13.1247

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