DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, September 15 Padelford C-401 3:45 pm

Analytic singularities of the dynamical zeta function for the billiard ball map

Vesselin Petkov (Université Bordeaux, France)

We study the dynamical zeta function Z_{D}(s) related to the periodic trajectories of the billiard flow for several disjoint strictly convex bodies in R^{3}. We show that the analytic properties of Z_{D}(s) close to the line of absolute convergence ℜs = s_{0} are similar to the behaviour close to the line ℜs = 1 of the inverse Q(s) = \frac{1}{R(s)} of the classical Riemann zeta function R(s).