DYNAMICAL SYSTEMS SEMINARS - A simple approach to rigorous approximation of invariant measures
Starts 7 Oct 2011 16:30
Ends 7 Oct 2011 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
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.