Distribution of resonances for hyperbolic surfaces
Spectral Theory
2013-10-17 v2 Mathematical Physics
Differential Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.1305.4850,
title = {Distribution of resonances for hyperbolic surfaces},
author = {David Borthwick},
journal= {arXiv preprint arXiv:1305.4850},
year = {2013}
}
Comments
28 pages, 29 figures; revised with minor corrections and one additional figure