Séminaire OrléansA Tour through Multiple Time Scale Dynamics
Christian Kuehn (Vienne)
Thursday 28 June 2012 14:00 - Orléans - Salle de Séminaire
An overview of multiple time scale systems and singular perturbation problems will be given. It is the goal of this talk to show the breadth of this field and outline some of its major techniques developed within the last two decades. First, I am going to briefly introduce the background for the geometric viewpoint for normally hyperbolic systems covering Fenichel theory and the notion of canards. Next, switchting between fast and slow systems will be considered using the Exchange Lemma. When normal hyperbolicity is lost the blow-up method for desingularization is employed. Then a collection of problems linking multiple time scales to numerical analysis, topological techniques, stochastic analysis and complex networks will be outlined. Each problem is motivated by models from applications.