A topological characterisation of holomorphic parabolic germs in the plane

Frédéric Le Roux (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Gambaudo and Pécou introduced the ``linking property'' to study the dynamics of germs of planar homeomorphims and provide a new proof of Naishul theorem in their paper "A topological invariant for volume preserving diffeomorphisms" (Ergodic Theory Dynam. Systems 15 (1995), no. 3, 535--541). In this paper we prove that the negation of Gambaudo-Pécou property characterises the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be defined, and it will turn out to be non trivial except for countably many conjugacy classes.

Mots clés: Rotation set; Surface; Parabolic fixed point.; Parabolic fixed point

Domaines: Systèmes dynamiques [math.DS]

Frédéric Le Roux. A topological characterisation of holomorphic parabolic germs in the plane. 2007. ⟨hal-00170681⟩