Year: 2026
Type: preprint
Abstract: We develop a new theory of thermodynamic formalism for non-compact flows, providing criteria for existence and uniqueness of equilibrium states, as well as ergodicity and a Gibbs property. These criteria include new versions of the expansivity and specification properties that hold for geodesic flows on non-compact negatively curved manifolds. Previous results on thermodynamic formalism for these geodesic flows were restricted by a pinched curvature condition, which we remove, allowing curvature to approach both $0$ and $-\infty$. Our results also apply to geodesic flows beyond the smooth setting, including locally CAT(-1) spaces.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1520159106, CAREER: Unifying approaches to non-uniform hyperbolicity, Hyperbolicity with Singularities and Coexistence via Smoothing, Hyperbolic behavior in dynamical systems: Higher-order phenomena beyond uniformity, G6403809984, New Directions in Thermodynamic Formalism for Geodesic Flows Beyond the Closed Riemannian Case, Advances in Ergodic Geometry
OpenAlex ID: W7165401190