Livsic theorems for connected Lie groups

Authors:
M. Pollicott and C. P. Walkden

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2879-2895

MSC (2000):
Primary 58F11; Secondary 58F15

DOI:
https://doi.org/10.1090/S0002-9947-01-02708-8

Published electronically:
March 12, 2001

MathSciNet review:
1828477

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Let be a hyperbolic diffeomorphism on a basic set and let be a connected Lie group. Let be Hölder. Assuming that satisfies a natural partial hyperbolicity assumption, we show that if is a measurable solution to a.e., then must in fact be Hölder. Under an additional centre bunching condition on , we show that if assigns `weight' equal to the identity to each periodic orbit of , then for some Hölder . These results extend well-known theorems due to Livsic when is compact or abelian.

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Additional Information

**M. Pollicott**

Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, U.K.

Email:
mp@ma.man.ac.uk

**C. P. Walkden**

Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, U.K.

Email:
cwalkden@ma.man.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-01-02708-8

Received by editor(s):
January 31, 1999

Received by editor(s) in revised form:
April 12, 2000

Published electronically:
March 12, 2001

Article copyright:
© Copyright 2001
American Mathematical Society