Boundary constructions of petals at the Wolff point in the parabolic case

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 $$\Re e(f''(\tau )) = 0$$ .