On distribution of the zeros of semi-classical zeta functions

Jeudi 5 novembre 2009 14:00-15:00 - Tsujii Masato - Kyushu University

Résumé : We discuss about spectral properties of transfer operators and related analytic properties of dynamical zeta functions for geodesic flows on negatively curved manifolds.
We first take Hilbert spaces contained in the space of distributions on the phase space so that they fit in the contact structure and in the hyperbolic structure of the flow.
Then we give the essential spectral radius of the transfer operators on them exactly in terms of the hyperbolicity exponent of the flow.
This result in particular implies that the semi-classical zeta function have only finitely many zeros on the right of the (epsilon neighborhood of) the imaginary axis.
I also like to discuss about the zeros on the neighborhood of the imaginary axis.

Lieu : bât. 425 - 121-123

On distribution of the zeros of semi-classical zeta functions  Version PDF
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