Regularity of solutions to the measurable Livsic equation

Pollicott, M.; Yuri, M.

doi:10.1090/S0002-9947-99-02383-1

Regularity of solutions to the measurable Livsic equation
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by M. Pollicott and M. Yuri PDF

Trans. Amer. Math. Soc. 351 (1999), 559-568 Request permission

Abstract:

In this note we give generalisations of Livsic’s result that a priori measurable solutions to cocycle equations must in fact be more regular. We go beyond the original continuous hyperbolic examples of Livsic to consider examples of this phenomenon in the context of:

[(a)] $\beta$-transformations;

[(b)] rational maps; and

[(c)] planar maps with indifferent periodic points.

Such examples are not immediately covered by Livsic’s original approach either due to a lack of continuity or hyperbolicity.

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