SDG meeting: Freddy Dumortier -- Relaxation oscillations in slow-fast systems

On Friday the 22nd of August, Freddy Dumortier (University of Hasselt) will talk at USyd
in Carslaw 273 at 4pm on 

"Relaxation oscillations in slow-fast systems” 

Abstract: The talk deals with two-dimensional slow-fast systems.  These systems depend
on a small parameter ε, and possibly also on other parameters, in a way that for
epsilon=0 the equation has a continuum of singular points.  Such systems can be studied
by means of Geometric Singular Perturbation Theory.  This theory essentially relies on
center manifold reduction.  The first to introduce it was Fenichel.  Traditional
Fenichel theory can however only be used near normally hyperbolic situations.  Around
1995 it became clear how the blow technique could extend the power of the theory to
including contact points.  Center manifolds, normal forms and blow-up permit to treat
singular perturbation problems by means of traditional methods from dynamical systems
theory.  In the talk we will only shortly recall the essential ingredients from the
theory.  We will mainly present a number of recent results concerning relaxation
oscillations for epsilon>0, epsilon small: their number, the bifurcations they undergo.
We will focus on the current state of the theory paying attention to remaining
problems.  The results come from a number of papers of Robert Roussarie, Peter De
Maesschalck and myself, inluding work in progress.  

Hope to see you all there, 

Georg