A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area

Autor:	Pohl, Anke D.
Rok vydání:	2014
Předmět:	Mathematics - Dynamical Systems Mathematical Physics Mathematics - Number Theory Primary: 37D40 37C30 Secondary: 37B10
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-015-2304-1
Popis:	We provide an explicit construction of a cross section for the geodesic flow on infinite-area Hecke triangle surfaces which allows us to conduct a transfer operator approach to the Selberg zeta function. Further we construct closely related cross sections for the billiard flow on the associated triangle surfaces and endow the arising discrete dynamical systems and transfer operator families with two weight functions which presumably encode Dirichlet respectively Neumann boundary conditions. The Fredholm determinants of these transfer operator families constitute dynamical zeta functions, which provide a factorization of the Selberg zeta function of the Hecke triangle surfaces. Comment: 23 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1404.3934 Zobrazit plný text záznamu View this record from Arxiv