Basic Concepts on Ergodic Teory

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