Renormalization in the Golden-Mean Semi-Siegel H\'enon Family: Non-Quasisymmetry

Jonguk Yang

Renormalization in the Golden-Mean Semi-Siegel H\'enon Family: Non-Quasisymmetry

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arxiv 1905.03357 v1 pith:LT2BJ4KS submitted 2019-05-08 math.DS math.CV

Jonguk Yang This is my paper · ORCID

classification math.DSmath.CV

keywords complexenongolden-meanquadraticanalogousboundarydiskfamily

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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 H\'enon maps of two complex variables.

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Structural Instability of Semi-Siegel H\'enon maps
math.DS 2019-08 conditional novelty 6.0 of 10

The golden-mean semi-Siegel Hénon family is not weakly J*-stable at any parameter, yielding Newhouse phenomenon and disconnected Julia sets on dense parameter sets.

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