The semiclassical zeta function for geodesic flows on negatively curved manifolds

16 Oct 2016  ·  Faure Frédéric, Tsujii Masato ·

We consider the semi-classical (or Gutzwiller-Voros) zeta function for $C^\infty$ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any $\tau>0$, that its zeros are contained in the union of the $\tau$-neighborhood of the imaginary axis, $|\Re(s)|<\tau$, and the region $\Re(s)<-\chi_0+\tau$, up to finitely many exceptions, where $\chi_0>0$ is the hyperbolicity exponent of the flow... Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law. read more

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Dynamical Systems