Title: Measure rigidity theorems in smooth dynamics
Speaker: Asaf Katz
Speaker Info: UMichigan
Classifying the invariant measures for a given dynamical system is a fundamental problem. In the field of homogeneous dynamics, several important theorems give us an essentially complete picture. Moving away from homogeneous dynamics - results are scarcer, mainly due to some profound difficulties carrying out the techniques used in homogeneous dynamics.Date: Tuesday, May 03, 2022
A recent development in Teichmuller dynamics - the celebrated magic wand theorem of Eskin-Mirzakhani, gives one such example and actually provides a technique - the factorization method - for proving such results in certain systems.
I will explain how one can implement the factorization method of Eskin-Mirzakhani in smooth dynamics, in order to achieve measure classification of u-Gibbs states for non-integrable Anosov actions. Moreover, I will try to explain some applications of the theorem, such as a pointwise equidistribution theorem for non-integrable systems and a result of Avila-Crovosier-Eskin-Potrie-Wilkinson-Zhang towards Gogolev's conjecture on actions on the 3D torus.