Quasi-compactness of transfer operators for contact Anosov flows

2008/06/04 by Tsujii, Masato · 1 citation
#37A25 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0806.0732

Abstract

For any C^r contact Anosov flow with r≥ 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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