A topological characterization of holomorphic parabolic germs in the plane
Volume 198 / 2008
Fundamenta Mathematicae 198 (2008), 77-94 MSC: 37E30, 37E45, 37F99. DOI: 10.4064/fm198-1-4
J.-M. Gambaudo and É. Pécou introduced the “linking property” in the study of the dynamics of germs of planar homeomorphisms in order to provide a new proof of Naishul's theorem. In this paper we prove that the negation of the Gambaudo–Pécou property characterizes 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 turns out to be non-trivial except for countably many conjugacy classes.