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Random Dynamics and a formula for Furstenberg, Kullback-Ledrappier Entropy

Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 14, 2015 (01:30 PM PDT - 02:20 PM PDT)
Speaker(s): Federico Rodriguez Hertz (Pennsylvania State University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • existence and uniqueness results

  • invariant measure

  • ergodic measure

  • Entropy formulas

  • mapping class groups

  • geometric group theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14247

Abstract

Joint with Aaron Brown, we found the following property for stationary measures of random composition of surface diffeomorphisms. Either the stable space is non-random, or the stationary measure is atomic or it is and SRB measure. This result generalize the work of Y. Benoist and J-F. Quint as well as the ones by A. Eskin and M. Mirzakhani to non-homogeneous, non affine setting.  In the meantime we found a formula for the Furstenberg or Kullback-Ledrappier entropy involving Lyapunov exponents and dimensions. In this talk I will describe the results and some consequences of it. 

Supplements
23530?type=thumb Hertz.Notes 186 KB application/pdf Download
Video/Audio Files

14247

H.264 Video 14247.mp4 288 MB video/mp4 rtsp://videos.msri.org/data/000/023/468/original/14247.mp4 Download
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