Dynamical Systems Seminar
Friday September 13th, 2019
Time: 2:30 PM - 3:30 PM
Title: Structural Stability in the Semi-Siegel Hénon Family
Speaker: Jonguk Yang, Stony Brook University
Location: Math Tower P-131
Abstract:
Consider the family of strongly dissipative quadratic Hénon maps with a semi-Siegel fixed point of golden-mean rotation number. Using a renormalization approach inspired by the work of Lyubich and Martens for Feigenbaum Hénon maps, we show that this family is structurally unstable. Combining this result with the work of Dujardin and Lyubich, we are able to conclude that the subset of semi-Siegel Hénon maps that 1) have infinitely many sinks, or 2) have a disconnected Julia set, each form a dense subset within the family.

This is joint work with M. Yampolsky