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

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

2011-12-27

arxiv.org/abs/1112.6023v1

Mathematics

Dynamical Systems

13 pages

Scientific paper

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.

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