A topological characterization of holomorphic parabolic germs in the plane

Frédéric Le Roux. "A topological characterization of holomorphic parabolic germs in the plane." Fundamenta Mathematicae 198.1 (2008): 77-94. <http://eudml.org/doc/282684>.

@article{FrédéricLeRoux2008,
abstract = {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.},
author = {Frédéric Le Roux},
journal = {Fundamenta Mathematicae},
keywords = {invariant petals; linking property; short trip property; parabolic homeomorphism; Leau-Fatou theorem},
language = {eng},
number = {1},
pages = {77-94},
title = {A topological characterization of holomorphic parabolic germs in the plane},
url = {http://eudml.org/doc/282684},
volume = {198},
year = {2008},
}

TY - JOUR
AU - Frédéric Le Roux
TI - A topological characterization of holomorphic parabolic germs in the plane
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 1
SP - 77
EP - 94
AB - 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.
LA - eng
KW - invariant petals; linking property; short trip property; parabolic homeomorphism; Leau-Fatou theorem
UR - http://eudml.org/doc/282684
ER -