Automorphisms of Ck\mathbb C^k with an invariant non-recurrent attracting Fatou component biholomorphic to C×(C)k1\mathbb C\times (\mathbb C^\ast)^{k-1}

  • Filippo Bracci

    Università di Roma Tor Vergata, Roma, Italy
  • Jasmin Raissy

    Université de Toulouse III Paul Sabatier, Toulouse, France
  • Berit Stensønes

    Norwegian University of Science and Technology, Trondheim, Norway
Automorphisms of $\mathbb C^k$ with an invariant non-recurrent attracting Fatou component biholomorphic to $\mathbb C\times (\mathbb C^\ast)^{k-1}$ cover
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Abstract

We prove the existence of automorphisms of Ck\mathbb C^k, k2k \geq 2, having an invariant, non-recurrent Fatou component biholomorphic to C×(C)k1\mathbb C \times (\mathbb C^\ast)^{k-1} which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. As a corollary, we obtain a Runge copy of C×(C)k1\mathbb C \times (\mathbb C^\ast)^{k-1} in Ck\mathbb C^k. The constructed Fatou component also avoids kk analytic discs intersecting transversally at the fixed point.

Cite this article

Filippo Bracci, Jasmin Raissy, Berit Stensønes, Automorphisms of Ck\mathbb C^k with an invariant non-recurrent attracting Fatou component biholomorphic to C×(C)k1\mathbb C\times (\mathbb C^\ast)^{k-1}. J. Eur. Math. Soc. 23 (2021), no. 2, pp. 639–666

DOI 10.4171/JEMS/1019