Basic Concepts on Ergodic Teory

Date: 
Friday, December 12, 2014
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)