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 disc Δ ⊂ 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 τ: f of non-automorphism type and \(\Re e(f''(\tau )) > 0\) or f injective of automorphism type, f∈C 3+ɛ(τ) and \(\Re e(f''(\tau )) = 0\).
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Partially supported by PRIN Proprietà geometriche delle varietà reali e complesse.
Partially supported by GNSAGA of the Istituto Nazionale di Alta Matematica, Rome.
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Bisi, C., Gentili, G. Boundary constructions of petals at the Wolff point in the parabolic case. J Anal Math 104, 1–11 (2008). https://doi.org/10.1007/s11854-008-0013-9
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DOI: https://doi.org/10.1007/s11854-008-0013-9