Random Dynamics and a formula for Furstenberg, Kullback-Ledrappier Entropy
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: MSRI: Simons Auditorium
existence and uniqueness results
invariant measure
ergodic measure
Entropy formulas
mapping class groups
geometric group theory
22E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
37A35 - Entropy and other invariants, isomorphism, classification
37A45 - Relations with number theory and harmonic analysis [See also 11Kxx]
14247
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.
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14247
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