Some basic notions and results in topological dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions, but which have to be put in the right setting, there are also new phenomena. Mostly for groupoids whose source map is not open (and there are many), some properties which were equivalent for group actions become distinct in this general framework; we illustrate this with various counterexamples.
Felipe Flores; Marius Măntoiu. Topological dynamics of groupoid actions. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 1005-1047. doi: 10.4171/ggd/687
@article{10_4171_ggd_687,
author = {Felipe Flores and Marius M\u{a}ntoiu},
title = {Topological dynamics of groupoid actions},
journal = {Groups, geometry, and dynamics},
pages = {1005--1047},
year = {2022},
volume = {16},
number = {3},
doi = {10.4171/ggd/687},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/687/}
}
TY - JOUR
AU - Felipe Flores
AU - Marius Măntoiu
TI - Topological dynamics of groupoid actions
JO - Groups, geometry, and dynamics
PY - 2022
SP - 1005
EP - 1047
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/687/
DO - 10.4171/ggd/687
ID - 10_4171_ggd_687
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%A Felipe Flores
%A Marius Măntoiu
%T Topological dynamics of groupoid actions
%J Groups, geometry, and dynamics
%D 2022
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%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/687/
%R 10.4171/ggd/687
%F 10_4171_ggd_687
