DYNAMICAL SYSTEMS SEMINARS - A simple approach to rigorous approximation of invariant measures
(UFRJ, Rio de Janeiro, Brazil)
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.
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