![Long-time existence of Brownian motion on configurations of two landmarks](/media/cache/video_light/uploads/video/2024-05-27_Habermann.mp4-f3c5e7a76e67422a67e6bc7b40a07b96-video-e3edec34d766217962b940b19f0e045e.jpg)
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Long-time existence of Brownian motion on configurations of two landmarks
By Karen Habermann
![Rigid geometric structures and their automorphism groups - Part 5](/media/cache/video_light/uploads/video/Capture%20d%E2%80%99%C3%A9cran%202024-06-20%20%C3%A0%2010.42.39.png)
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Rigid geometric structures and their automorphism groups - Part 5
By Karin Melnick
Appears in collection : Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups
We will review some dynamical systems associated to an Anosov representation and draw some geometric conclusions. More precisely, we will review topics such as the Patterson-Sullivan Theory for these representations, the critical hypersurface, dynamical intersection, dynamics of the \theta-Weyl-chamber flow, and finally directional-conicality and generalizations. We will then consider the approach of dominated sequences and draw conclusions on the regularity of limit sets. Some relevant references are lecture 1: Babillot-Ledrappier, Bridgeman-Canary-Labourie-S., Burger-Landesberg-Lee-Oh, Carvajales, Chow-Sarkar, Dey-Kapovich, Ledrappier, Lee-Oh, S. lecture 2: Bochi-Potrie-S., Pozzetti-S., Pozzetti-S.-Wienhard, Zhang-Zimmer.