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Analytic singularities of the dynamical zeta function

Vesselin Petkov

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Recommended by P Cvitanovic

We study the dynamical zeta function ZD(s) related to the periodic trajectories of the billiard flow for several disjoint strictly convex bodies in BbbR3. We show that the analytic properties of ZD(s) close to the line of absolute convergence Re s = s0 are similar to the behaviour close to the line Re s = 1 of the inverse Q(s) = 1/R(s) of the classical Riemann zeta function R(s).


PACS

02.30.Sa Functional analysis

02.10.De Algebraic structures and number theory

MSC

35P25 Scattering theory for PDE (See also 47A40)

11Mxx Zeta and L-functions: analytic theory

Subjects

Mathematical physics

Dates

Issue 6 (November 1999)

Received 21 October 1998, in final form 3 September 1999



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