El Kacimi Alaoui, A.; Hattab, H.; Salhi, E. Remarks about some groups of homomorphisms of metric spaces. (Remarques sur certains groupes d’homéomorphismes d’espaces métriques.) (French) Zbl 1074.37009 JP J. Geom. Topol. 4, No. 3, 225-242 (2004). 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 \(\mathbb{S}^1\). Cited in 7 Documents 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 Keywords:minimal groups; periodic points; periodic orbits; circle maps; equicontinuous group of homeomorphisms; orientation preserving homeomorphisms PDFBibTeX XMLCite \textit{A. El Kacimi Alaoui} et al., JP J. Geom. Topol. 4, No. 3, 225--242 (2004; Zbl 1074.37009)