We prove the existence of automorphisms of C-k , k >= 2, having an invariant, non-recurrent Fatou component biholomorphic to C x (C*)(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 x (C*)(k-1) in C-k. The constructed Fatou component also avoids k analytic discs intersecting transversally at the fixed point.
Bracci, F., Raissy, J., Stensones, B. (2021). Automorphisms of C-k with an invariant non-recurrent attracting Fatou component biholomorphic to C x (C*)(k-1). JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 23(2), 639-666 [10.4171/JEMS/1019].
Automorphisms of C-k with an invariant non-recurrent attracting Fatou component biholomorphic to C x (C*)(k-1)
Bracci, F
;
2021-01-01
Abstract
We prove the existence of automorphisms of C-k , k >= 2, having an invariant, non-recurrent Fatou component biholomorphic to C x (C*)(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 x (C*)(k-1) in C-k. The constructed Fatou component also avoids k analytic discs intersecting transversally at the fixed point.| File | Dimensione | Formato | |
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