×

Remarks about some groups of homomorphisms of metric spaces. (Remarques sur certains groupes d’homéomorphismes d’espaces métriques.) (French) Zbl 1074.37009

Summary: We study some qualitative properties of an equicontinuous group of homeomorphisms of a metric space. Examples showing the validity limit of these results are given. We also give a new elementary proof of the fact that there exists a deformation retract from the group \(\text{Homéo}_+(\mathbb{S}^1)\) of orientation preserving homeomorphisms of the circle \(\mathbb{S}^1\) on its Lie subgroup \(\mathbb{S}^1\).

MSC:

37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37C35 Orbit growth in dynamical systems
37E10 Dynamical systems involving maps of the circle
PDFBibTeX XMLCite