Renormalization in the Golden-Mean Semi-Siegel Hénon Family: Universality and Non-Rigidity (BA 1190)
Speaker:
Jonguk Yang, University of Toronto
Date and Time:
Thursday, July 20, 2017 - 11:00am to 11:30am
Location:
Bahen Building, Room 1190
Abstract:
In their recent work, Gaidashev and Yampolsky showed that appropriately defined renormalizations of a sufficiently dissipative golden-mean semi-Siegel Hénon map converge super-exponentially fast to a degenerate one-dimensional renormalization fixed point.
It turns out that the asymptotic two-dimensional form of such a renormalization sequence is universal, and is parameterized by the average Jacobian. Using this result, we show that the boundary of a golden-mean Siegel disk of a dissipative Hénon map is non-rigid.