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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.

5 votes
1 answer
177 views

Connection between rates of convergence in ergodic theorems and spectral gap property

I've been reading Quantitative ergodic theorems and their number-theoretic applications By Gorodnik and Nevo (arXiv:1304.6847). Early on, there is a comment on rates of convergence in the mean ergodic …
16 votes
3 answers
1k views

What are some interesting examples of non-classical dynamical systems? (Group action other t...

By classical dynamical system, I mean a measure space together with a measurable action of the integers or the reals. Of course, this action is often interpreted as evolution with respect to discrete …