Unique equilibrium states for geodesic flows in nonpositive curvature

• Published in: Geometric and functional analysis Vol. 28; no. 5; pp. 1209 - 1259
• Main Authors: Burns, K., Climenhaga, V., Fisher, T., Thompson, D. J.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.10.2018; Springer Nature B.V
• Subjects: Analysis; Curvature; Mathematics; Mathematics and Statistics; Silicon; Uniqueness; 37C40; 37D40; Equilibrium states; 37D35; 37D25; Topological pressure; Geodesic flow

We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar multiples of the geometric potential on the interval ( - ∞...