Appears in collection : Etats de la recherche: Arithmetic, Algebraic and Analytics Dynamics / Etats de la recherche: Dynamique arithmétique, algébrique, et analytique

It is a fundamental problem to measure the complexity of a dynamical system. In this lecture, we discuss this problem for arithmetic dynamics in terms of topology, algebra and arithmetic. In particular, the notion of dynamical degrees, which can be viewed as an algebraic analogy of “entropy”, plays a key role. We will see how it applies to study the orbits, periodic points and action of cohomologies.