Examines escape rate spectra in hyperbolic surfaces, indicating their transient behavior.
Given a Fuchsian group Γ , we introduce escape rate spectra associated with Γ to investigate the transient behavior of the geodesic flow on the hyperbolic surface D/Γ . Our definition is motivated by Bishop’s linear escape set. In the special case when D/Γ is a hyperbolic Z -covering of a surface uniformized by a generalized Schottky group, we completely determine the escape rate spectra by the convex conjugate of a generalized Poincaré exponent.
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Jaerisch et al. (2026) studied this question.
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