Category: List of Bases 2011 Throughout the year  RESEARCH IN MATHEMATICS 

Title:

DYNAMICAL SYSTEMS SEMINARS - A simple approach to rigorous approximation of invariant measures

Start Time:

15:30

Location:

ICTP (Leonardo da Vinci Building Luigi Stasi Seminar Room)

Contact:

A. Bergamo

Speaker(s):

Isaia Nisoli (UFRJ, Rio de Janeiro, Brazil)

Description:

Piecewise expanding maps of the interval are one of the simplest examples of chaotic behaviour in dynamics; in 1973 Lasota and Yorke proved that these maps admit a finite set of ergodic absolutely continuous invariant measures.

In this joint work with Stefano Galatolo we implement a numerical algorithm that, using a discretization of the transfer operator, permits us to compute the invariant measure for a topologically transitive expanding map of the interval rigorously, thanks to a spectral stability result by Liverani.

In this seminar I want to give an overview of the tecniques and the results we use, to show the main ideas which lie behind our work.