[Todos CMAT] Seminario Sistemas Dinámicos

Rafael Potrie rpotrie en cmat.edu.uy
Mie Ago 20 18:52:33 UYT 2008


Escribo para comunicar que el próximo Martes 26/8 a las 14:30 tendremos una
charla en el IMERL a cargo de Tanya Yarmola del Courant Institute.
Son todos bienvenidos.

Sigue titulo y resumen de la charla:

Tanya Yarmola
Courant Institute, New York University

Title: Invariant Measures for Degenerate Random Perturbations of
Discrete-Time Dynamical Systems

Abstract: Random perturbations of dynamical systems is an important tool in
modeling noise and other types of uncontrolled fluctuations. In many
real-life systems, fluctuations do not occur everywhere or uniformly in
all directions; some of these situations can be modeled by {\it
localized, degenerate noise}. In this thesis (advisor: Lai-Sang Young),
we focus on random
perturbations of discrete-time dynamical systems that occur in a single
direction; we call these {\it rank one perturbations.} The aim of this
work is to study whether such perturbations lead to invariant measures
that are absolutely continuous with respect to Lebesgue measure.

This study is based on the premise that when the dynamics are rich
enough, they tend to mix the different directions after a number of
iterates. Thus barring unfortunate coincidences, one should expect even
rank one perturbations to have absolutely continuous invariant
measures. We introduce a very general condition that ensures that all
the invariant measures for the perturbed system are absolutely


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