On cohomological theory of dynamical zeta functions

Masato Tsujii

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arXiv · 1805.11992

On cohomological theory of dynamical zeta functions

Masato Tsujii

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Abstract

We discuss about the conjectural cohomological theory of dynamical zeta functions in the case of general Anosov flows. Our aim is to provide a functional-analytic framework that enables us to justify the basic part of the theory rigorously. We show that the zeros and poles of a class of dynamical zeta functions, including the semi-classical (or Gutzwiller-Voros) zeta functions, are interpreted as eigenvalues of the generators of some transfer operators acting on the leaf-wise de Rham cohomology spaces of the unstable foliation.

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Masato Tsujii. 2018-05-30. On cohomological theory of dynamical zeta functions. https://arxiv.org/abs/1805.11992

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