Topological dynamics of groupoid actions

  • Felipe Flores

    Universidad de Chile, Santiago, Chile
  • Marius Măntoiu

    Universidad de Chile, Santiago, Chile
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Abstract

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.

Cite this article

Felipe Flores, Marius Măntoiu, Topological dynamics of groupoid actions. Groups Geom. Dyn. 16 (2022), no. 3, pp. 1005–1047

DOI 10.4171/GGD/687