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.
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Daniele Galli (2024) studied this question.
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