Title: SRB measures without symbolic dynamics or dominated splittings
Speaker: Vaughn Climenhaga
Speaker Info: University of Maryland
Many important dynamical systems admit an SRB measure: an invariant probability measure with non-zero Lyapunov exponents that is absolutely continuous along unstable manifolds, and thus bears witness to the chaotic nature of the system. Many more systems are believed to admit such a measure based on numerical evidence, but a complete rigorous understanding is still out of reach.Date: Monday, May 16, 2011
Most of the standard constructions of SRB measures rely on symbolic dynamics (via Markov partitions or inducing schemes) or on the existence of a dominated splitting. We describe a procedure for constructing SRB measures that does not require either of these, and relies instead on constructing measurable cone families for which a certain asymptotic rate of "usable hyperbolicity" is positive for Lebesgue-typical trajectories. We give examples of systems with no dominated splitting for which no inducing schemes or Markov partitions are known to exist, but for which our methods prove existence of an SRB measure.
This is joint work with Dmitry Dolgopyat and Yakov Pesin.