CAPA: Physical measures and measure rigidity for partially hyperbolic systems with two dimensional center

  • Datum: –16.15
  • Plats: Ångströmlaboratoriet 74118
  • Föreläsare: Davi Obata
  • Arrangör: Matematiska institutionen
  • Kontaktperson: Rodrigo Goncalves Schaefer
  • Seminarium

For a dynamical system, a physical measure is an ergodic invariant measure that captures the asymptotic statistical behavior of the orbit of a set of points that is significant for the Lebesgue measure. A natural question in the theory is to know when such measures exist.

It is expected that a ”typical” system with enough ”hyperbolicity” (such as partial hyperbolicity) should have such a measure. For partially hyperbolic systems, if a physical measure exists it must be a special type of measure called u-Gibbs. However, u-Gibbs measures are not necessarily physical.

In this talk I will explain (in a non technical way) a measure rigidity result for u-Gibbs measures that I obtain for a certain class of partially hyperbolic systems with two dimensional center. In particular, I prove that in this class of systems either an u-Gibbs measure is physical or it has some rigid structure. This gives some light in proving that a ”typical” partially hyperbolic system with two dimensional center has a physical measure.