# FELLESKOLLOKVIUM FREDAG 19. MAI 2006

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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

EB/HB/BJ/PAØ Hovedsiden