Example of a diffeomorphism for which the special ergodic theorem doesn't hold
arXiv:1112.6023
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.
15 pages, 7 figures