Open sets of partially hyperbolic systems having a unique SRB measure

CDSNS Colloquium
Friday, December 10, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Zoom (see additional notes for link)
Davi Obata – U Chicago – daviobata@uchicago.edu
Alex Blumenthal

Please Note:

For a dynamical system, a physical measure is an ergodic invariant measure that captures the asymptotic statistical behavior of the orbits of a set with positive 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 measures. A special type of physical measure is the so-called hyperbolic SRB (Sinai-Ruelle-Bowen) measure. Since the 70`s the study of SRB measures has been a very active topic of research. 

In this talk, we will see a new example of open sets of partially hyperbolic systems with two dimensional center having a unique SRB measure.  One of the key features for these examples is a rigidity result for a special type of measure (the so-called u-Gibbs measure) which allows us to conclude the existence of the SRB measures.