Ergodic and statistical properties of smooth systems

Abstract: We will discuss some classical ergodic (Bernoulli, K-property, positive entropy...) and statistical (limit theorems, quantitative mixing...) properties of smooth dynamical systems. We will discuss their flexibility (i.e. non-trivial examples of systems which satisfy some but not all of them) and rigidity (i.e. some properties imply other). We will mostly focus on two results: 1) exponential mixing implies Bernoulli 2) existence of zero entropy systems satisfying a central limit theorem.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University