Edmond Covanov

Ruelle and Policott's introduction of resonances in the 1980s marked a significant advance in understanding the 
long-term behaviour of Axiom A flows. These Ruelle resonances, defined as the discrete spectrum of the transfer
operator on some sophisticated anisotropic Banach space, provide a nice framework to describe the convergence 
towards equilibrium.

In this talk, we investigate the notion of resonance in the context of Anosov-type systems, which are known to 
be C1 stable. Arnold's cat map serves as a central example, offering a clear setting to examine the spectral 
properties of the transfer operator and their connection to the decay of correlations. By analysing the transfer 
operator of an Anosov map in some appropriate functional space, we show the existence of resonances and how 
they encode the statistical properties of the dynamics.