Ergodic Theory and Computability

Speaker : Valérie Berthé


We question the relevance of ergodic theory for the study of computer trajectories for dynamical systems. We focus here on finite and periodic orbits in the framework of arithmetic dynamics. Arithmetic dynamics provides explicit expansions of real numbers (or of vectors) which have a dynamical meaning in order to produce symbolic codings of dynamical systems preserving their arithmetic structure. This includes numeration dynamical systems, digital expansions and generalized continued fraction maps.