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Presented By: Geometry Seminar - Department of Mathematics

RTG Seminar on Geometry, Topology and Dynamics: Absolute continuity of stationary measure

Homin Lee

In this talk, we discuss about the smooth random dynamical systems on surfaces. Based on the measure rigidity work by Aaron Brown and Federico Rodriguez Hertz, we know that a stationary measure has SRB property unless there is a certain obstruction. Here, SRB property implies that, morally, the measure is 'absolutely continuous' along 1 dimensional piece.
In this talk, we consider about a different mechanism to get ‘measure rigidity’ which promote SRB to absolute continuity using ‘transversality' motivated by Tsujii’s works on partially hyperbolic endomorphisms and Bernoulli convolution.
The talk is based on a joint work in progress with Aaron Brown, Davi Obata, and Yuping Ruan.

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