What question did this study set out to answer?

The study aims to define and analyze escape rate spectra for hyperbolic surfaces associated with Fuchsian groups.

April 10, 2026

Escape rate spectra for hyperbolic Z-covers of Schottky surfaces

Key Points

The study aims to define and analyze escape rate spectra for hyperbolic surfaces associated with Fuchsian groups.
Introduced escape rate spectra for a given Fuchsian group.
Investigated the geodesic flow on hyperbolic surfaces.
Determined the spectra using convex conjugate of the Poincaré exponent.
Escape rate spectra are fully determined for hyperbolic Z-covers of surfaces uniformized by Schottky groups.
The results are based on Bishop's linear escape set and Poincaré exponents.

Abstract

Abstract Given a Fuchsian group, we introduce escape rate spectra associated with to investigate the transient behavior of the geodesic flow on the hyperbolic surface D/. Our definition is motivated by Bishop’s linear escape set. In the special case when D/ 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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Authors

Johannes Jaerisch

ZIYU LIU

Journals

Ergodic Theory and Dynamical Systems

Actions

Institutions

Nagoya University

Shanghai Dianji University

References and Citations

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Building similarity graph...

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Escape rate spectra for hyperbolic Z-covers of Schottky surfaces

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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