Locating Ruelle–Pollicott resonances* *This work was partially supported by the PRIN Grant ‘Regular and stochastic behaviour in dynamical systems’ (PRIN 2017S35EHN). LC and OB acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006. We thank Péter Bálint, Viviane Baladi, Oscar Bandtlow, Giovanni Forni, Stefano Galatolo, Daniele Galli, Thomas Gilbert, Marco

Abstract

We study the spectrum of transfer operators associated to various dynamical systems. Our aim is to obtain precise information on the discrete spectrum. To this end we propose a unitary approach. We consider various settings where new information can be obtained following different branches along the proposed path. These settings include affine expanding Markov maps, uniformly expanding Markov maps, non-uniformly expanding or simply monotone maps, hyperbolic diffeomorphisms. We believe this approach could be greatly generalised.