יום חמישי, ט' נאדר ב', תשס"ג

Thursday, 13th March 2003, 4:00 pm

Mathematics Building, Lecture Hall 2

Genadi Levin

(HU)

"Universality of unimodal maps with infinite criticality"

** Abstract: ** The universality in one-dimensional dynamics
was discovered numerically by Feigenbaum and Coullet-Tresser in the late
1970s. (Very soon, similar observations were made for some important high-dimensional
non-linear dynamical systems such as Lorenz system of differential equations.)
It is described by fixed points of renormalization operators *R* of
the form

*RH=a\circ H^p \circ a^{-1},*

where *a* is a re-scaling. For every real number *c>1*, the
universality is observed in a space of maps *H* with a single critical
point of order *c*. In a recent joint work with Greg Swiatek, we prove
that the family *H_c* of corresponding fixed-point maps of *R*
for different criticalities *c* converges as *c* goes to infinity.

In the talk, which is going to be elementary, we describe the history of the area including a rigorous computer-assisted approach to the above problem by Eckmann and Wittwer, 1985.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2002-03

List of talks, 2001-02

List of talks, 2000-01

List of talks, 1998-99

List of talks, 1997-98