This is part of a series of collaborative meetings between the universities of Bristol, Exeter, Loughborough, Manchester, Queen Mary, St. Andrews and Warwick, supported by a Scheme 3 grant from the London Mathematical Society.
Abstract: Equilibrium states for geodesic flows over compact rank 1 non-positive curvature manifolds and sufficiently regular potential functions were studied by Burns, Climenhaga, Fisher and myself. We showed that if the higher rank set does not carry full topological pressure then the equilibrium state is unique. In this talk, I will describe some recent results on the dynamical properties of these unique equilibrium states. We show that these equilibrium states have the Kolmogorov property (joint with Ben Call), and that approximations of the equilibrium states by regular closed geodesics asymptotically satisfy a type of Central Limit Theorem (joint with Tianyu Wang). Time permitting, I will explain some of the main ideas behind the proofs, focusing on the MME case to ease the exposition.
The talks will take place via Zoom. The link will be sent a few days before the meeting to the UK ergodic theory and dynamical systems mailing list. To subscribe to this mailing list go here.
For more information, please contact:
Tom Kempton
Department of Mathematics
University of Manchester
Manchester M13 9PL
email: thomas.kempton@manchester.ac.uk
For details of other meetings in the series, click here.