Boundary construction 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 ∆ ⊂ 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(f′′ (τ)) > 0, or f injective of automorphism type, f ∈ C3+ǫ(τ) and Re(f′′ (τ)) = 0.