A topological characterisation of holomorphic parabolic germs in the plane

Details A topological characterisation of holomorphic parabolic germs in the plane A topological characterisation of holomorphic parabolic germs in the plane

2007-09-10

arxiv.org/abs/0709.1398v1

Mathematics

Dynamical Systems

Scientific paper

Gambaudo and P\'ecou 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-P\'ecou 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.

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