Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions
Abstract
Given a holomorphic iterated function scheme with a finite symmetry group $G$, we show that the associated dynamical zeta function factorizes into symmetryreduced analytic zeta functions that are parametrized by the unitary irreducible representations of $G$. We show that this factorization implies a factorization of the Selberg zeta function on symmetric $n$funneled surfaces and that the symmetry factorization simplifies the numerical calculations of the resonances by several orders of magnitude. As an application this allows us to provide a detailed study of the spectral gap and we observe for the first time the existence of a macroscopic spectral gap on Schottky surfaces.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.6134
 Bibcode:
 2014arXiv1407.6134B
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Dynamical Systems;
 58J50;
 37C30;
 81Q50
 EPrint:
 To appear in "Journal of Spectral Theory"