Abstract:We develop the theory of equilibrium states via specification properties for a wide class of continuous flows on complete separable metric spaces. An important motivating example is geodesic flow over negatively curved manifolds without pinching assumptions and geodesic flow over CAT(-1) spaces. Since our phase space is non-compact, we need to establish all the basic definitions and results to make this theory work, including a suitable notion of topological pressure and fundamental results such as the variational principle. We introduce a notion of strong positive recurrence in this setting and use it as a criterion to prove the existence and uniqueness of an equilibrium state.
From: Daniel J. Thompson [view email]
[v1]
Thu, 18 Jun 2026 15:56:13 UTC (105 KB)
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