Asaf Katz

University of Michigan

Measure rigidity of Anosov flows via the factorization method

Ergodic Theory and Dynamical Systems Seminar

25th February 2021, 2:00 pm – 3:00 pm
Online, via Zoom

Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a negatively curved surface. In the talk we will introduce those flows and their dynamical behavior. Moreover, we show how the factorization method, pioneered by Eskin and Mirzakhani in their groundbreaking work about measure rigidity for the moduli space of translation surfaces, can be adapted to smooth ergodic theory and in particular towards the study of Anosov flows. Using this adaption, we show that for a quantitatively non-integrable Anosov flow, every generalized u-Gibbs measure is absolutely continuous with respect to the whole unstable manifold. In the talk I will discuss the factorization method, the relations to previous works (Eskin-Mirzakhani, Eskin-Lindenstrauss) and the result together with some examples and applications.

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