Geodesic
A topological characterization of holomorphic parabolic germs in the plane
Frédéric Le Roux1
1 Laboratoire de Mathématiques CNRS UMR 8628 Université Paris-Sud, Bât. 425 91405 Orsay Cedex, France
Fundamenta Mathematicae, Tome 198 (2008) no. 1, pp. 77-94

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm198-1-4
Keywords: m gambaudo cou introduced linking property study dynamics germs planar homeomorphisms order provide proof naishuls theorem paper prove negation gambaudo cou property characterizes topological dynamics holomorphic parabolic germs consequence rotation set germs surface homeomorphisms around fixed point defined turns out non trivial except countably many conjugacy classes

Frédéric Le Roux 1

1 Laboratoire de Mathématiques CNRS UMR 8628 Université Paris-Sud, Bât. 425 91405 Orsay Cedex, France 
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Frédéric Le Roux. A topological characterization of holomorphic
 parabolic germs in the plane. Fundamenta Mathematicae, Tome 198 (2008) no. 1, pp. 77-94. doi: 10.4064/fm198-1-4

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