- A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms
- Galli, Daniele <1995>
Subject
- MAT/07 Fisica matematica
Description
- Given a transitive Anosov diffeomorphism on a closed manifold it is known that, for smooth enough observables, the system is mixing w.r.t. the measure of maximal entropy. Therefore, it makes sense to investigate the speed of decay of correlations and to look for the so-called Ruelle-Pollicott resonances, in order to determine a complete asymptotics for the decay of correlations. In this thesis we are able to find the first terms of that asymptotics and to prove an estimate for the speed of decaying of correlations. The proof is based on a surprising connection between the action of a transfer operator on suitable anisotropic Banach spaces of currents and the action induced by the Anosov map on the de Rham cohomology.
Date
- 2023-06-30
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-29501
Galli, Daniele (2023) A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica