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Topological Wiener–Wintner ergodic theorems and a random L2 ergodic theorem

Published online by Cambridge University Press:  19 September 2008

Peter Walters
Peter Walters
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
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Abstract

We give some topological ergodic theorems inspired by the Wiener-Wintner ergodic theorem. These theorems are used to give results for uniquely ergodic transformations and to study unique equilibrium states for shift maps. These latter results give random L2 ergodic theorems for a finite set of commuting measure-preserving transformations.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996, pp. 179 - 206
Copyright
Copyright © Cambridge University Press 1996

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