• Datum: 18 maj, kl. 10.15
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Remus Radu, University of Toronto
  • Kontaktperson: Michael Benedicks
  • Seminarium

Två föredrag av Remus Radu:

10.15-11.15: Dynamics of complex Henon maps with a semi-neutral fixed point
11.30-12.30: Hedgehogs in higher dimensions

Remus Radu, University of Toronto 10.15-11.15

Title: Dynamics of complex Henon maps with a semi-neutral fixed point

Abstract: Complex Henon maps are a special case of polynomial automorphisms of C^2 which arise from physical applications and are central objects in the study of holomorphic dynamics in 2D. In this talk we give a unified treatment on Henon maps with a semi-neutral fixed point (i.e. which has one eigenvalue of absolute value one and one eigenvalue of absolute value less than one). As in 1D, we can distinguish three cases: semi-parabolic, semi-Siegel and semi-Cremer.  We outline the different (non-hyperbolic) behavior in each case, discuss recent progress, and make analogies to one-dimensional dynamics.

Remus Radu, University of Toronto 11.30-12.30

Title:  Hedgehogs in higher dimensions 

Abstract: Hedgehogs in dimension one were introduced by Perez-Marco in the '90s to study linearization properties and dynamics of holomorphic univalent germs of (C, 0) with a neutral fixed point. In this talk we discuss hedgehogs and their dynamics for germs of holomorphic diffeomorphisms of (C^n, 0) with a fixed point at the origin with exactly one neutral eigenvalue. We show how to use quasiconformal theory to transport results from one complex dimension to higher dimensions. This is based on joint work with T. Firsova, M. Lyubich, and R. Radu