T. M. Jonassen :
"The dynamics of the Henon map"

The classical Henon mapping is a two-parameter family of mappings of the plane first studied by M. Henon in 1976 where he found numerical evidence for a strange attractor. It turned out that it was very difficult to provide a rigorous mathematical proof for the existence of such objects.

I consider some of L. Carlesons contributions to dynamical systems theory, in particular the proof of the existence of strange attractors in the Henon family published in The dynamics of the Henon map in Annals of Mathematics in 1991 (with M. Benedicks). As this paper is a tour de force analysis of the Henon family, I will focus on the ideas, and not the technicalities. Carlesons work provides the first example of a genuinely nonuniformly hyperbolic attractor, and the techniques introduced in this paper have later led to the construction of Sinai-Ruelle-Bowen (SRB) measures for such objects, and recently led to a more complete theory for a class of nonuniformly hyperbolic attractors. The talk is intended for an audience not working in the field of dynamical systems.

1300-1400 i pausearealet i 7. etage