English

A transcendental H\'enon map with an oscillating wandering Short $\mathbb{C}^2$

Complex Variables 2019-01-23 v1 Dynamical Systems

Abstract

Short C2\mathbb{C}^2'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 C2\mathbb{C}^2. The superexponential rate of attraction is not obtained at single iterations, but along consecutive oscillations.

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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}
}