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

Autor:	Benini, Anna Miriam, Saracco, Alberto, Zedda, Michela
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Complex Variables 37F80 32H50 37F10
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.02756 Zobrazit plný text záznamu View this record from Arxiv