In the same spirit of the classical Leau-Fatou flower theorem, we prove the existence of a petal, with vertex at the Wolff point, for a holomorphic self-map $f$ of the open unit disk $\Delta \subset \mathbb{C}$ of parabolic type. The result is obtained in the framework of two interesting dynamical situations which require different kinds of regularity of $f$ at the Wolff point $\tau:$ $f$ of non-automorphism type and $Re(f''(\tau))>0$ or $f$ injective of automorphism type, $f \in C^{3+\epsilon} (\tau)$ and $Re(f''(\tau))=0.$
Boundary Constructions of Petals at the Wolff Point in the Parabolic Case.
BISI, Cinzia;
2008
Abstract
In the same spirit of the classical Leau-Fatou flower theorem, we prove the existence of a petal, with vertex at the Wolff point, for a holomorphic self-map $f$ of the open unit disk $\Delta \subset \mathbb{C}$ of parabolic type. The result is obtained in the framework of two interesting dynamical situations which require different kinds of regularity of $f$ at the Wolff point $\tau:$ $f$ of non-automorphism type and $Re(f''(\tau))>0$ or $f$ injective of automorphism type, $f \in C^{3+\epsilon} (\tau)$ and $Re(f''(\tau))=0.$File in questo prodotto:
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