Document Type
Lecture
Publication Date
10-13-2016
Abstract
One of the world leaders in dynamical systems theory, Jean-Christophe Yoccoz died last month. I will give a general mathematical audience talk on rigidity in dynamics, an area to which he contributed a lot. Rigidity theory of circle diffeomorphisms is a classic topic in dynamical systems largely developed by Herman and Yoccoz. Rigidity, in this context, refers to a phenomenon that every two maps, within a given topological equivalence class, are smoothly conjugate to each other (i.e., the same up to a smooth coordinate change). A natural approach to Herman's theory involves renormalization, a powerful idea that connects many different areas of mathematics and physics. I will discuss the main ideas of renormalization and rigidity theory and give an overview of the results (including some of my own) for circle maps and generalized interval exchange transformations (the latter being generalizations of circle maps, recently introduced by Marmi, Moussa and Yoccoz). The talk will be fully understandable to graduate students without any previous knowledge in dynamics.
Relational Format
presentation
Recommended Citation
Kocić, Saša, "Rigidity in dynamics: in memory of J.-C. Yoccoz" (2016). Dynamical Systems Seminar. 4.
https://egrove.olemiss.edu/math_dynamical/4
