Bernoulli Lecture IV   18 November 2014

17:15 - 18:30

Lecturers

Marc Diener, Université de Nice

Francine Diener, Université de Nice

Maciej Krupa, INRIA

HOW CANARDS WERE BORN AND WHAT THEY BECAME


In order to test how to take advantage of infinitesimals, as introduced by Non Standard Analysis, G. Reeb suggested in 1977 to consider the behaviour of solutions of one of the most well known slow-fast dynamics, the Van der Pol Equation. This initiated a process of experimental Mathematics, with mutual stimulation between abstract theory and numerical experiments that was called “La chasse aux canards”. Marc Diener will explain first why this duck’s hunt was  more difficult than expected due to the fact that two canard’s values differ from an exponentially small amount. We know now that this short live of the canards is the sign that the canard’s values  have as asymptotic expansion a divergent series with coefficients growing as n! (called Gevrey series). Francine Diener will explain why, as Poincaré already said, divergence in this context is not a bad news by a good one. Since the seventies, the canards was the starting points of numerous researches as the phenomenon is present in higher dimension and in more complex dynamics.  Martin Krupa will give some examples of these researches.

Name University Dates of visit
Marc Diener Université de Nice 18/11/2014 - 18/11/2014
Francine Diener Université de Nice 18/11/2014 - 18/11/2014
Maciej Krupa INRIA 18/11/2014 - 18/11/2014
Total Guests : 3
Name University Dates of visit
Total Guests : 0