Structural instability of semi-Siegel Hénon maps

We show that the dynamics of sufficiently dissipative semi-Siegel complex Hénon maps with golden-mean rotation number is not J-stable in a very strong sense. By the work of Dujardin and Lyubich, this implies that the Newhouse phenomenon occurs for a dense Gδ set of parameters in this family. Another...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 389; p. 107900
Main Authors Yampolsky, Michael, Yang, Jonguk
Format Journal Article
LanguageEnglish
Published Elsevier Inc 08.10.2021
Subjects
Newhouse phenomenon
Renormalization
Siegel disc for Henon map
Structural instability in dynamical systems
Newhouse phenomenon
Renormalization
Siegel disc for Henon map
Structural instability in dynamical systems
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Summary:We show that the dynamics of sufficiently dissipative semi-Siegel complex Hénon maps with golden-mean rotation number is not J-stable in a very strong sense. By the work of Dujardin and Lyubich, this implies that the Newhouse phenomenon occurs for a dense Gδ set of parameters in this family. Another consequence is that the Julia sets of such maps are disconnected for a dense set of parameters.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107900