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arXiv · 1112.6023

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

Dmitry Ryzhov
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Abstract

In this work we present an example of C^\infty-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure μbut for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a continuous function ϕand a positive constant αsuch that the following holds: the set of the initial points for which the Birkhoff time averages of the function ϕdiffer from its μ--space average by at least αhas zero Lebesgue measure but full Hausdorff dimension.

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Dmitry Ryzhov. 2012-08-20. Example of a diffeomorphism for which the special ergodic theorem doesn't hold. https://arxiv.org/abs/1112.6023

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