Anosov diffeomorphisms of open surfaces

Snir Ben Ovadia, Jonathan DeWitt

Published 2024-07-23Version 1

We study the existence of Anosov diffeomorphisms on complete open surfaces. We show that under the assumptions of density of periodic points and uniform geometry that such diffeomorphisms have a system of Margulis measures, which are a holonomy invariant and dynamically invariant system of measures along the stable and unstable leaves. This shows that there can be no such diffeomorphism with a global product structure.