Example of a diffeomorphism for which the special ergodic theorem doesn't hold

In this work we present an example of C^\infty-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure \mu but for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a continuous function \phi and a positive constant \alpha such t...

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Bibliographic Details
Published in:arXiv.org 2012-08
Main Author: Ryzhov, Dmitry
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Ergodic processes
Isomorphism
Theorems
Online Access:Get full text
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Summary:In this work we present an example of C^\infty-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure \mu but for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a continuous function \phi and a positive constant \alpha such that the following holds: the set of the initial points for which the Birkhoff time averages of the function \phi differ from its \mu--space average by at least \alpha has zero Lebesgue measure but full Hausdorff dimension.
ISSN:2331-8422