Sarah Bray – The dynamics of non-strictly convex Hilbert geometries

Carte non disponible

Date/heure
Date(s) - 28/03/2014
11 h 00 min - 12 h 30 min

Catégories Pas de Catégories


Any open, properly convex domain $\Omega$ in $\R\P^n$ admits a Hilbertmetric, compatible with a Finsler norm. Of particular interest are compactquotients of $\Omega$ by discrete subgroups of $\PGL(n+1,\R)$. Thedynamical, topological, algebraic, and regularity properties of suchquotients with the line flow have been exhaustively studied by Benoist andothers in the case that $\Omega$ is strictly convex and consequently$\delta$-hyperbolic. My agenda is to expand previous studies to the convexbut not strictly convex case for $\Omega$. In this talk, I will introduce aclass of higher dimensional examples, constructed by Benoist, which exhibitsome hyperbolicity properties. I will explicitly describe the topologicaland ergodic dynamical properties of the line flow on the projectivetriangle, which plays a focal role as an obstruction to hyperbolicity inthe non-strictly convex examples of Benoist. I will assure you that weexpect this obstruction to be surmountable. http://sites.tufts.edu/poincare/meet-the-team/sarah-bray/ Sarah Bray[

Sarah Bray – The dynamics of non-strictly convex Hilbert geometries

Carte non disponible

Date/heure
Date(s) - 28/03/2014
11 h 00 min - 12 h 30 min

Catégories Pas de Catégories


Any open, properly convex domain $\Omega$ in $\R\P^n$ admits a Hilbert metric, compatible with a Finsler norm. Of particular interest are compact quotients of $\Omega$ by discrete subgroups of $\PGL(n+1,\R)$. The dynamical, topological, algebraic, and regularity properties of such quotients with the line flow have been exhaustively studied by Benoist and others in the case that $\Omega$ is strictly convex and consequently $\delta$-hyperbolic. My agenda is to expand previous studies to the convex but not strictly convex case for $\Omega$. In this talk, I will introduce aclass of higher dimensional examples, constructed by Benoist, which exhibit some hyperbolicity properties. I will explicitly describe the topological and ergodic dynamical properties of the line flow on the projective triangle, which plays a focal role as an obstruction to hyperbolicity in the non-strictly convex examples of Benoist. I will assure you that we expect this obstruction to be surmountable. http://webhosting.math.tufts.edu/sbray/ Sarah Bray[