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