A transcendental H\'enon map with an oscillating wandering Short $\mathbb{C}^2$
Complex Variables
2019-01-23 v1 Dynamical Systems
Abstract
Short 's were constructed in [F] as attracting basins of a sequence of holomorphic automorphisms whose rate of attraction increases superexponentially. The goal of this paper is to show that such domains also arise naturally as autonomous attracting basins: we construct a transcendental H\'enon map with an oscillating wandering Fatou component that is a Short . The superexponential rate of attraction is not obtained at single iterations, but along consecutive oscillations.
Keywords
Cite
@article{arxiv.1901.07394,
title = {A transcendental H\'enon map with an oscillating wandering Short $\mathbb{C}^2$},
author = {Leandro Arosio and Luka Boc Thaler and Han Peters},
journal= {arXiv preprint arXiv:1901.07394},
year = {2019}
}