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: | |
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: |