Quasi-compactness of transfer operators for contact Anosov flows

Details Quasi-compactness of transfer operators for contact Anosov flows Quasi-compactness of transfer operators for contact Anosov flows

2008-06-04

arxiv.org/abs/0806.0732v3

Mathematics

Dynamical Systems

59pages, no figure

Scientific paper

For any $C^r$ contact Anosov flow with $r\ge 3$, we construct a scale of Hilbert spaces, which are embedded in the space of distributions on the phase space and contain all $C^r$ functions, such that the transfer operators for the flow extend to them boundedly and that the extensions are quasi-compact. Further we give explicit bounds on the essential spectral radii of the extensions in terms of the differentiability r and the hyperbolicity exponents of the flow.

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