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# Midwest Dynamics and Group Actions Seminar

On ergodic and statistical properties of smooth systems
Monday, April 5, 2021
4:00-5:00 PM
Off Campus Location
We will recall some basic ergodic and statistical properties such as: ergodicity, (quantitative) mixing, K property, Bernoullicity, central limit theorem. We will be interested in rigidity and flexibility of these properties for smooth diffeomorphisms preserving a smooth measure. Our main rigidity result is that C^{1+\alpha} smooth diffeomorphisms which are exponentially mixing are Bernoulli (joint with D. Dolgopyat and F.Rodriguez-Hertz). For flexibility results we show existence of C^r smooth systems which satisfy the (non-trivial) central limit theorem and are of zero entropy. Moreover we show that there are smooth K, non-Bernoulli systems which satisfy (non-trivial) central limit theorem (joint with D. Dolgopyat, C. Dong, P.Nandori).