Develops topological pressure, variational principle, and strong positive recurrence to prove existence and uniqueness of equilibrium states for non-compact flows with specification.
On the non-expansiveness of the geodesic flow on surfaces with cusps
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abstract
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of strong stable sets in the dynamical sense that do not coincide with the stable horocycles. When the surface has finite volume, this phenomenon is typical.
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math.DS 1years
2026 1verdicts
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Thermodynamic formalism for non-compact systems with expansivity and specification
Develops topological pressure, variational principle, and strong positive recurrence to prove existence and uniqueness of equilibrium states for non-compact flows with specification.