Polskie Towarzystwo Matematyczne, Oddzial Warszawski
Instytut Matematyczny PAN, Centrum Banacha

zapraszaja na

Wyklad-Kolokwium we czwartek, 18 listopada o godz. 16:30
w sali 321 Instytutu Matematycznego PAN, Sniadeckich 8 (III pietro).

Profesor Mitsuhiro Shishikura (Kyoto University)

"Dynamics and Renormalization"

Wyklad poprzedzi polgodzinne spotkanie przy kawie i ciastkach.
Po wykladzie, o 17.45, odbedzie sie Walne Zebranie Warszawskiego Oddzialu Polskiego Towarzystwa Matematycznego Serdecznie zapraszamy!

Abstract

The renormalization is an important idea in dynamical systems, hich proved effective in the studies of bifurcations and rigidities, etc. t was first introduced for unimodal maps on the interval in order to
explain the universality of period doubling bifurcation sequences. Key idea is to take an appropriate subset of the phase space and consider the first return map to this subset (and rescale the set if necessary). This defines a meta-dynamics on the space of certain dynamical systems. This idea has been applied in many settings and surprisingly the meta-dynamics is often a simpler one, such as a contraction or a hyperbolic system, from which people were able to derive conclusion on the
original dynamical systems. In this talk, we discuss the general idea of renormalization and some specific cases, in particular, the renormalization associated to irrationally indifferent fixed points of holomorphic functions.