Specters in the jungle of anisotropic Banach spaces
Viviane Baladi (CNRS & Institut de Mathématiques de Jussieu, Paris)

The spectrum (or, as Google translate would have it, the specter) of a (Ruelle-Perron-Frobenius) transfer operator contains valuable information on the properties of an ergodic chaotic dynamical system - but only if one lets it act on a good Banach space! In the past fifteeen years, dynamicists (and more recently semi-classically oriented mathematicians) have introduced several types of anisotropic distributions. In this non-technical presentation, we will enjoy a small tour in the jungle of these spaces, discovering the advantages and shortcomings of the various existing definitions.