Hénon mappings with biholomorphic escaping sets

For any complex Hénon map H P , a : x y ↦ P ( x ) - a y x , the universal cover of the forward escaping set U + is biholomorphic to D × C , where D is the unit disk. The vertical foliation by copies of C descends to the escaping set itself and makes it a rather rigid object. In this note, we give ev...

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Bibliographic Details
Published inComplex analysis and its synergies Vol. 3; no. 1; pp. 1 - 18
Main Authors Bonnot, Sylvain, Radu, Remus, Tanase, Raluca
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.11.2017
Springer Nature B.V
Subjects
Algebraic Geometry
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Partial Differential Equations
Biholomorphisms
Hénon mappings
Escaping sets
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Summary:For any complex Hénon map H P , a : x y ↦ P ( x ) - a y x , the universal cover of the forward escaping set U + is biholomorphic to D × C , where D is the unit disk. The vertical foliation by copies of C descends to the escaping set itself and makes it a rather rigid object. In this note, we give evidence of this rigidity by showing that the analytic structure of the escaping set essentially characterizes the Hénon map, up to some ambiguity which increases with the degree of the polynomial P .
ISSN:2197-120X
2524-7581
2197-120X
DOI:10.1186/s40627-017-0010-9