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arXiv:2405.17045 [math.DS]AbstractReferencesReviewsResources

A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms

Daniele Galli

Published 2024-05-27Version 1

We investigate Ruelle-Pollicott resonances of Anosov diffeomorphisms with respect to the measure of maximal entropy. We highlight a profound connection between resonances and eigenvalues of the action induced by the dynamics on de Rham cohomology. We finally exploit this relation to get information about the Ruelle-Pollicott asymptotics of the correlation function and establish a cohomological bound for the speed of mixing of Anosov diffeomorphisms.

Comments: 58 pages
Categories: math.DS, math.DG
Subjects: 37A25, 37D20, 37C30, 14F40
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