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Invariant escaping Fatou components with two rank-one limit functions for automorphisms of
${\mathbb C}^2$
Published online by Cambridge University Press: 22 November 2021
Abstract
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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- © The Author(s), 2021. Published by Cambridge University Press
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