Preparatory Workshop

Date and place: Wednesday, June 7, 13:00-16:30, rook 1016.

The preparatory workshop will outline the basic concepts in ergodic theory and discuss the Lyapunov's exponents.

13:00-13:45 Jakub Byszewski (UJ) A brief introduction to ergodic theory

Abstract: The aim of the talk is to introduce some basic concepts and questions of ergodic theory. We will discuss a number of examples. The talk will be elementary and available to undergraduate students (3rd year and higher).
 
13.45-14.45 pizza
 
14.45-15.30 Wojciech Słomczyński (UJ) Differential equations, Lyapunov exponents and the Oseledets multiplicative ergodic theorem

Abstract: We define the characteristic Lyapunov exponents that for a system of linear ODEs describe the behaviour of its solutions and for a smooth dynamical system characterizes the rate of separation of infinitesimally close trajectories. We also formulate the Multiplicative Ergodic Theorem proved by Oseledets in 1968. From this theorem it follows that the Lyapunov exponents do not depend on the choice of the initial point from a set of full ergodic measure.
 
15.45-16.30 Michał Rams (IM PAN) TBA

Abstract: