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Elastic Graphs for Main Molecule Matings
Caroline Davis, Jasmine Powell, Rebecca R. Winarski +1
Recent work of Dylan Thurston gives a condition for when a post-critically finite branched self-cover of the sphere is equivalent to a rational map. We apply D. Thurston's positive…
Structural Instability of Semi-Siegel Hénon maps
Michael Yampolsky, Jonguk Yang
We show that the dynamics of sufficiently dissipative semi-Siegel complex Hénon maps with golden-mean rotation number is not -stable in a very strong sense. By the work of Dujar…
Renormalization in the Golden-Mean Semi-Siegel Hénon Family: Non-Quasisymmetry
Jonguk Yang
For quadratic polynomials of one complex variable, the boundary of the golden-mean Siegel disk must be a quasicircle. We show that the analogous statement is not true for quadratic…
Renormalization in the Golden-Mean Semi-Siegel Hénon Family: Universality and Non-Rigidity
Jonguk Yang
It was recently shown by Gaidashev and Yampolsky that appropriately defined renormalizations of a sufficiently dissipative golden-mean semi-Siegel Hénon map converge super-exponent…