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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Published in:Ergodic theory and dynamical systems 2023-02, Vol.43 (2), p.401-416
Main Authors: BENINI, ANNA MIRIAM, SARACCO, ALBERTO, ZEDDA, MICHELA
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Language:English
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Automorphisms
Behavior
Invariants
Original Article
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description 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.
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subjects Automorphisms
Behavior
Invariants
Original Article
title Invariant escaping Fatou components with two rank-one limit functions for automorphisms of ${\mathbb C}^2
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