Bowen and Margulis independently proved in the 70s that closed geodesics on compact hyperbolic surfaces equidistribute towards the measure of maximal entropy. From a homogeneous dynamics point of view, this measure is the quotient of the Haar measure on $\mathrm{PSL}(2,\mathbb{R})$ modulo some discrete cocompact sugroup.
In a joint work with Jialun Li, we investigate the higher rank setting of this problem by taking a higher rank Lie group (like $\mathrm{SL}(d,\mathbb{R})$ for $d\geq 3$) and by studying the dynamical properties of geodesic flows in higher rank: the so-called Weyl chamber flows and their induced diagonal action. We obtain an equidistribution formula of periodic tori (instead of closed orbits of the geodesic flow).
By Jean-François Quint
By Jean-François Quint
By Pierre-Louis Blayac
By Jean-François Quint
By Pratyush Sarkar
By Sam Edwards
By Minju Lee
By Andrés Sambarino
By Minju Lee
By Giuseppe Martone
By Andrés Sambarino
By Leon Carvajales
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Chao Li
By Albert Schwarz
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Amine Marrakchi
By Francesca Arici
