Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances

Details Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances

2008-02-13

arxiv.org/abs/0802.1780v3

Open Math. Journal, vol. 1, 35--81, (2008)

Nonlinear Sciences

Chaotic Dynamics

48 pages

Scientific paper

In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable anisotropic Sobolev spaces and which govern the decay of dynamical correlations, can be treated as the quantum resonances of open quantum systems in the Aguilar-Baslev-Combes theory or the more recent Helffer-Sjostrand phase-space theory.

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