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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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)
$\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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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: http://dx.doi.org/10.1090/S0002-9947-99-02383-1
PII: S 0002-9947(99)02383-1
Received by editor(s): August 5, 1996
Article copyright: © Copyright 1999 American Mathematical Society