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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-1-4,
author = {Fr\'ed\'eric Le Roux},
title = {A topological characterization of holomorphic parabolic germs in the plane},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {77-94},
zbl = {1160.37012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-1-4}
}
Frédéric Le Roux. A topological characterization of holomorphic parabolic germs in the plane. Fundamenta Mathematicae, Tome 201 (2008) pp. 77-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-1-4/