Document Type
Lecture
Publication Date
10-1-2015
Abstract
Rigidity theory of circle diffeomorphisms is a classic topic in dynamical systems which started with the work of Arnol’d and was largely developed by Herman, Yoccoz and others. Rigidity, in this context, refers to a phenomenon that every two maps, within a given topological equivalence class, are smoothly conjugate to each other. A natural approach to Herman’s theory involves renormalization, one of the most powerful ideas in mathematics. I will discuss main ideas of renormalization and rigidity theory and give an overview of the recent results on rigidity of circle diffeomorphisms with a break, i.e., circle diffeomorphisms with a single singular point where the derivative has a jump discontinuity. These results can be considered an extension of Herman’s theory on the linearization of circle diffeomorphisms.
Relational Format
presentation
Recommended Citation
Kocić, Saša, "Renormalization and rigidity theory of circle diffeomorphisms with a break" (2015). Dynamical Systems Seminar. 11.
https://egrove.olemiss.edu/math_dynamical/11
