November 23-25, 2005 -- 3:30 p.m.
(Courant Institute of Mathematical Sciences)
A mathematical theory of strange attractors
held at the Fields Institute
Attractors play an important role in dynamical systems theory
as they capture the large-time behavior of many orbits. I will
report on some recent developments in the analysis of a class
of attractors. These attractors occur naturally. They are chaotic,
or "strange", in the sense that they have complex geometric
structures, and their dynamics are unpredictable, generating statistics
that resemble those from random stochastic processes.
The first lecture is an overview aimed at a general audience.
In the second hour, I will try to paint a geometric picture of
these attractors, and in the third, I will demonstrate how to
verify the existence of attractors of this type in several situations,
including periodically forced limit cycles and Hopf bifurcations
for ODEs and evolutionary PDEs.
Thematic Program Home page
The Fields Institute Coxeter Lecture Series (CLS) brings a leading
mathematician to the Institute to give a series of three lectures
in the field of the current thematic program. The first talk is
an overview for a general mathematical audience, postdoctoral
fellows and graduate students. The other two talks are chosen,
in collaboration with the organizers of the thematic program,
to target specialists in the field.