## 2006.312: Livsic theorems for connected Lie groups

2006.312:
M. Pollicott and C. P. Walkden
(2001)
*Livsic theorems for connected Lie groups.*
Transactions of the American Mathematical Society, 353 (7).
pp. 2879-2895.
ISSN 1088-6850

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DOI: 10.1090/S0002-9947-01-02708-8

## Abstract

Let $\phi$ be a hyperbolic diffeomorphism on a basic set $\Lambda$ and let $G$ be a connected Lie group. Let $f : \Lambda \rightarrow G$ be Hölder. Assuming that $f$ satisfies a natural partial hyperbolicity assumption, we show that if $u : \Lambda \rightarrow G$ is a measurable solution to $f=u\phi \cdot u^{-1}$ a.e., then $u$ must in fact be Hölder. Under an additional centre bunching condition on $f$, we show that if $f$ assigns `weight' equal to the identity to each periodic orbit of $\phi$, then $f = u\phi \cdot u^{-1}$ for some Hölder $u$. These results extend well-known theorems due to Livsic when $G$ is compact or abelian.

Item Type: | Article |
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Subjects: | MSC 2000 > 58 Global analysis, analysis on manifolds |

MIMS number: | 2006.312 |

Deposited By: | Miss Louise Stait |

Deposited On: | 16 August 2006 |

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