Boundary constructions of petals at the Wolff point in the parabolic case (Q940781)

In this paper, in the spirit of the classic Leau-Fatou flower theorem, the authors show the existence of a petal, with vertex at the Wolff point, for a holomorphic self-map \(f\) of the open unit disc \(\Delta\subset \mathbb{C}\) 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 \(\mathfrak{Re}(f''(\tau))>0\) or \(f\) injective of automorphism type, \(f\in C^{3+\varepsilon}(\tau)\) and \(\mathfrak{Re}(f''(\tau))=0\).