Tohoku Mathematical Journal
2007
June
SECOND SERIES VOL. 59, NO. 2

Tohoku Math. J.
59 (2007), 167-202

Title MEROMORPHIC EXTENSIONS OF A CLASS OF ZETA FUNCTIONS FOR TWO-DIMENSIONAL BILLIARDS WITHOUT ECLIPSE

Dedicated to Professor Yoichiro Takahashi on his sixtieth birthday
Author Takehiko Morita

(Received September 6, 2004, revised November 21, 2006)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 37C30; Secondary 37D50, 37F15.
Key words and phrases. Dynamical zeta functions, thermodynamic formalism, dispersing billiards without eclipse.

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