Invariant escaping Fatou components with two rank-one limit functions for automorphisms of ${\mathbb C}^2

We construct automorphisms of ${\mathbb C}^2$ , and more precisely transcendental Hénon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank one. We also prove a general growth lemma for the norm of points in orbits belonging to inva...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2023-02, Vol.43 (2), p.401-416
Main Authors: BENINI, ANNA MIRIAM, SARACCO, ALBERTO, ZEDDA, MICHELA
Format: Article
Language:English
Subjects:
Automorphisms
Behavior
Invariants
Original Article
Online Access:Get full text
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Summary:We construct automorphisms of ${\mathbb C}^2$ , and more precisely transcendental Hénon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank one. We also prove a general growth lemma for the norm of points in orbits belonging to invariant escaping Fatou components for automorphisms of the form $F(z,w)=(g(z,w),z)$ with $g(z,w):{\mathbb C}^2\rightarrow {\mathbb C}$ holomorphic.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.125