We prove the uniqueness of equilibrium states for certain potentials satisfying the Bowen property for two flows related to geodesic flows on surfaces with sufficient hyperbolicity. Our first result is the uniqueness of equilibrium states for Hölder continuous potentials and the geometric potential for products of geodesic flows of rank one surfaces. Second, with Keith Burns and Todd Fisher, we prove the uniqueness of equilibrium states for Hölder potentials for the geodesic flow on the unit tangent bundle of surfaces with negative curvature outside of spherical caps. As a consequence, this flow has a unique measure of maximal entropy. This is the first result for uniqueness of equilibrium states for geodesic flows for metrics with conjugate points.

Creator

• McEnroe, Rachel Maxine

DOI

• https://doi.org/10.21985/n2-h5fb-cn57

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15743
• etdadmin_upload_844617

Keyword

• conjugate points
• hyberbolic dynamics
• measure of maximal entropy
• geodesic flow
• equilibrium state
• thermodynamic formalism

Date created

• 2021-01-01

Resource type

• Dissertation

Rights statement

• In Copyright