PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Stephanie Zerby, Anatole Katok, Federico Rodriguez Hertz.

Title:Dynamics of dissipative polynomial automorphisms of C^2
Seminar:Center for Dynamics and Geometry Colloquium
Speaker:Mikhail Lyubich, SUNY Stony Brook
Abstract:
Two-dimensional complex dynamics displays a number of phenomena that are not observable in dimension one. However, if f is moderately dissipative then there are deeper similarities between the two fields. In particualar, a nearly complete classification of periodic Fatou components has been recently obtained: Theorem 1 (joint with Han Peters): Any periodic component of the Fatou set is either an attracting basin or parabolic basin, or the basin of a rotation domain (Siegel disk or Herman ring). In complex and real one-dimensional world, structurally stable maps are dense. In dimension two this fails because of the Newhouse phenomenon caused by homoclinic tangencies. Palis conjectured that in the real two-dimensional case this is the only reason for failure. We prove a complex version of this conjecture: Theorem 2 (joint with Romain Dujardin): Any moderately dissipative polynomial automorphism of C^2 is either ``weakly stable" or it can be approximated by a map with homoclinic tangency.

Room Reservation Information

Room Number:MB114
Date:10 / 14 / 2014
Time:02:30pm - 03:30pm