The main purpose of the present paper is to show that a class of dynamical zeta functions associated with the so-called two-dimensional open billiard without eclipse have meromorphic extensions to the half-plane consisting of all complex numbers whose real parts are greater than a certain negative number. As an application, we verify that the zeta function for the length spectrum of the corresponding billiard table has the same property.
Publié le : 2007-05-14
Classification:
Dynamical zeta functions,
thermodynamic formalism,
dispersing billiards without eclipse,
37C30,
37D50,
37F15
@article{1182180733,
author = {Morita, Takehiko},
title = {Meromorphic extensions of a class of zeta functions for two-dimensional billiards without eclipse},
journal = {Tohoku Math. J. (2)},
volume = {59},
number = {1},
year = {2007},
pages = { 167-202},
language = {en},
url = {http://dml.mathdoc.fr/item/1182180733}
}
Morita, Takehiko. Meromorphic extensions of a class of zeta functions for two-dimensional billiards without eclipse. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp. 167-202. http://gdmltest.u-ga.fr/item/1182180733/