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arXiv · 2011.02756

Invariant escaping Fatou components with two rank 1 limit functions for automorphisms of $\mathbb{C}^2$

Anna Miriam Benini·Alberto Saracco·Michela Zedda
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Abstract

We construct automorphisms of $\mathbb{C}^2$, and more precisely transcendental H\'enon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank 1. 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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Anna Miriam Benini, Alberto Saracco, Michela Zedda. 2020-11-05. Invariant escaping Fatou components with two rank 1 limit functions for automorphisms of $\mathbb{C}^2$. https://arxiv.org/abs/2011.02756

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