Junyi Xie: Complexity theory in arithmetic dynamical systems - Lecture 3

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. CONFERENCE Recording during the thematic meeting : «Arithmetic, Algebraic and Analytics Dynamics » the January 24, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area