David Parmenter

Cones on leaves: exponential convergence to the Margulis measure via an unstable transfer operator

In this talk I'll prove that for a uniformly hyperbolic diffeomorphism, the pull back of the leaf volume on a pushed forward piece of unstable manifold converges exponentially fast to the Margulis measure (the unstable measure of maximal entropy). In order to do this I'll introduce notions of Birkhoff cones, transfer operators and prove an unstable analogue of the Ruelle-Perron-Frobenius theorem.