Distribution of resonances for hyperbolic surfaces

Abstract

We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation of the zeta function for Schottky groups. Our particular focus is on three aspects of the resonance distribution that have attracted attention recently: the fractal Weyl law, the spectral gap, and the concentration of decay rates.

28 pages, 29 figures; revised with minor corrections and one additional figure

References in corpus (6)

• Fractal Weyl laws for chaotic open systems
• Experimental Observation of the Spectral Gap in Microwave n-Disk Systems
• Weyl asymptotics: From closed to open systems
• Lifetime statistics in chaotic dielectric microresonators
• Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
• Density and localization of resonances for convex co-compact hyperbolic surfaces