PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Anatole Katok.

Title:Invariant measures for interval maps with critical points and singularities
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Stefano Luzzatto, Imperial College
Abstract:
We address the classical problem of the existence of absolutely continuous invariant measures in the setting of interval maps. This question has been investigated extensively over the last several decades and we now have a very good understanding in the setting of piecewise expanding maps and in the setting of smooth maps with critical points. However, the co-existence of critical points and singularities (discontinuities with possibly unbounded derivative) brings new technical issues and these have only started to be addressed over the last ten years or so. The subject is interesting from both a conceptual and a technical point of view as it combines two distinct causes of "non-uniform" hyperbolicity which can, at least in this one-dimensional setting, be treated in a unified way from a technical point of view. In this talk I will review existing results on maps with critical points and singularities and present a recent result which has been obtained together with V. Araujo and M. Viana.

Room Reservation Information

Room Number:MB106
Date:04 / 21 / 2008
Time:03:35pm - 05:35pm