Short C-2's were constructed in [5] 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 Henon map with an oscillating wandering Fatou component that is a Short C-2. The superexponential rate of attraction is not obtained at single iterations, but along consecutive oscillations.
Arosio, L., Thaler, L., Peters, H. (2021). A transcendental Henon map with an oscillating wandering Short C2. MATHEMATISCHE ZEITSCHRIFT, 299(1-2), 357-372 [10.1007/s00209-020-02677-4].
A transcendental Henon map with an oscillating wandering Short C2
Arosio, L;
2021-01-01
Abstract
Short C-2's were constructed in [5] 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 Henon map with an oscillating wandering Fatou component that is a Short C-2. The superexponential rate of attraction is not obtained at single iterations, but along consecutive oscillations.| File | Dimensione | Formato | |
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