Analytic continuation of a dynamical zeta function under a Diophantinecondition

Frédéric Naud

doi:10.1088/0951-7715/14/5/305

Nonlinearity

Analytic continuation of a dynamical zeta function under a Diophantine condition

Frédéric Naud¹

Published 9 July 2001 • Published under licence by IOP Publishing Ltd
Nonlinearity, Volume 14, Number 5 Citation Frédéric Naud 2001 Nonlinearity 14 995 DOI 10.1088/0951-7715/14/5/305

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¹ Laboratoire de Mathématiques Pures, Université Bordeaux 1, 33405 Talence, France

Dates

Received 26 April 2000
Published 9 July 2001

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Abstract

We study a dynamical zeta function Z_D(s) related to the periodic orbits of an open billiard flow for several disjoint convex bodies in Bbb R ³. We show that under a generic Diophantine condition, there exists an analytic continuation of Z_D(s) in a polynomially decreasing neighbourhood of the line of absolute convergence.

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