Geometry, Topology and Dynamics Seminar
Daniel Thompson
The Ohio State University
Specification and strong positive recurrence for flows on complete metric spaces
Abstract: We extend Bowen’s specification approach to thermodynamic formalism to flows on complete separable metric spaces. The key point, particularly for the existence of a finite equilibrium state, is a Strong Positive Recurrence (SPR) assumption. As one application, we establish that for a sufficiently regular potential with SPR for the geodesic flow on a geometrically finite locally CAT(-1) space, there exists a unique equilibrium state. Examples of CAT(-1) spaces range from manifolds with negative curvature bounded above by -1, and at the other extreme, graphs and trees equipped with a notion of length. This is joint work with Vaughn Climenhaga and Tianyu Wang.
Thursday December 4, 2025 at 11:00 AM in 427 SEO