Quasi-compactness of transfer operators for contact Anosov flows

Abstract

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.

59pages, no figure

References in corpus (1)

• Ruelle-Perron-Frobenius spectrum for Anosov maps

Cited by in corpus (3)

• Fractal Weyl law for the Ruelle spectrum of Anosov flows
• Asymptotic spectral gap for open partially expanding maps
• Classical limit theorems and high entropy MIXMAX random number generator