CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

8 décembre 2020 de 10 h 00 à 11 h 00 (heure de Montréal/Miami) Réunion Zoom

CRM-CAMP COLLOQUIUM: A complete proof of the Feigenbaum conjectures

Séminaire par Jean-Pierre Eckmann (University of Geneva, Switzerland)

In the late 1970s, Mitchell Feigenbaum discovered the universality of bifurcations in one-parameter families of maps. This universality was explained with a fixed point equation, and a flow in the space of all one-parameter families of maps. With Peter Wittwer, I showed in 1987 a rigorous proof of this phenomenon, using a "computer assisted" proof of the Feigenbaum conjectures. I will explain what are the somehow unconventional issues of this computer assisted proof, and how they are solved. Please keep in mind that this is quite old stuff, and a more modern implementation of the ideas would be much easier now than it was over 30 years ago.