Regularity of solutions to

the measurable Livsic equation

Authors:
M. Pollicott and M. Yuri

Journal:
Trans. Amer. Math. Soc. **351** (1999), 559-568

MSC (1991):
Primary 58Fxx

MathSciNet review:
1621702

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Abstract | References | Similar Articles | Additional Information

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)
- -transformations;
- (b)
- rational maps; and
- (c)
- planar maps with indifferent periodic points.

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Additional Information

**M. Pollicott**

Affiliation:
Department of Mathematics, Manchester University, Manchester, M13 9PL, England

Email:
mp@ma.man.ac.uk

**M. Yuri**

Affiliation:
Department of Business Administration, Sapporo University, 3-jo, 7-chome, Nishioka, Toyohira-ku, Sapporo 062, Japan

Email:
yuri@math.sci.hokudai.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-99-02383-1

Received by editor(s):
August 5, 1996

Article copyright:
© Copyright 1999
American Mathematical Society