Equidistribution of Periodic Tori

  • Thi Dang (Laboratoire de Mathématique d’Orsay)
E2 10 (Leon-Lichtenstein)


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 PSL(2, 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 SL(d, R) for d ≥ 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).

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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