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Renormalization and Siegel disks for complex H\'enon maps

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arxiv 1604.07069 v6 pith:ZCPLIQJB submitted 2016-04-24 math.DS

Denis Gaidashev , Remus Radu , Michael Yampolsky This is my paper · ORCID
classification math.DS
keywords mapsdisksenonrenormalizationsiegelcomplexdissipativegolden-mean
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We use hyperbolicity of golden-mean renormalization of dissipative H\'enon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex H\'enon maps with golden-mean rotation number are topological circles. Conditionally on an appropriate renormalization hyperbolicity property, we derive the same result for Siegel disks of H\'enon maps with all eventually periodic rotation numbers.

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  1. 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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