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Livšic regularity for Markov systems

Published online by Cambridge University Press:  22 September 2005

HENK BRUIN ,
MARK HOLLAND  and
MATTHEW NICOL
HENK BRUIN
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK (e-mail: h.bruin@surrey.ac.uk, mark.holland@surrey.ac.uk)
MARK HOLLAND
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK (e-mail: h.bruin@surrey.ac.uk, mark.holland@surrey.ac.uk)
MATTHEW NICOL
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: nicol@math.uh.edu)
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Abstract

We prove measurable Livšic theorems for dynamical systems modelled by Markov towers. Our regularity results apply to solutions of cohomological equations posed on Hénon-like mappings and a wide variety of non-uniformly hyperbolic systems. We consider both Hölder cocycles and cocycles with singularities of prescribed order.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 6 , December 2005 , pp. 1739 - 1765
Copyright
2005 Cambridge University Press

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