Title - Measure rigidity of Anosov flows via the factorization method.

Abstract: Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a Riemann 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 first part of the talk I will present the main result and how it relates to the previous works using this technique (Eskin-Mirzakhani, Eskin-Lindenstrauss).

In the second part I will discuss some of the technical details related to the Eskin-Mirzakhani technique.

Abstract: Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a Riemann 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 first part of the talk I will present the main result and how it relates to the previous works using this technique (Eskin-Mirzakhani, Eskin-Lindenstrauss).

In the second part I will discuss some of the technical details related to the Eskin-Mirzakhani technique.

## Date:

Wed, 25/12/2019 - 13:30 to 15:30

## Location:

Ross 70