# Basic Concepts on Ergodic Theory (Part 2)

Date:

Friday, March 6, 2015

Room:

204

Speaker:

Sina Türeli (PhD student of mathematics, SISSA)

Abstract:

In this talk (one or two talks depending on how it goes) I will outline basic concepts about ergodic theory, Boltzmann's ergodic hyphothesis and the concept of a deterministic system behaving in a probabilistic manner. I will start by shortly demonstrating with simple and concrete examples how does a mathematician think of probability. Then I will explain important parts of ergodic theorem; that is how space, time averages and mean visit times are related to invariance and ergodicity. With these in hand, I will discuss these result regarding Boltzmann's ergodic hyphothesis and explain the concept of an ergodic system having "probabilistic behaviour

References:

- Fundamentos da Teoria Ergódica- Viana (freely available in http://w3.impa.br/~viana/out/ite.pdf)
- Ergodic Theory and Differentiable Dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
- An Introduction to Ergodic Theory (Graduate Texts in Mathematics)