Abstract
Two types of recurrence sets are introduced for inverse semigroup partial actions
in topological spaces. Some applications to the basic dynamical properties of
the action are indicated, covering topics as topological transitivity, limit points
and periodic points. We then explore the connections of these recurrence sets
with similar notions for related types of imperfect symmetries (prefix inverse
semigroup expansions, partial group and groupoid actions).
Reference14 articles.
1. "[1] J. Auslander, Minimal Flows and Their Extensions. North-Holland Mathematics Studies 153, North-Holland, Amsterdam, 1988.
2. [2] V.M. Beuter and L.G. Cordeiro, The dynamics of partial inverse semigroup actions. J. Pure Appl. Algebra 224 (2018), 3, 917-957.
3. [3] A. Buss and R. Exel, Inverse semigroup expansions and their actions on C∗-algebras. Illinois J. Math. 56(2012), 4, 1185-1212.
4. [4] J. de Vries, Elements of Topological Dynamics. Mathematics and its Applications 257, Kluwer Acad. Publ., Dordrecht, 1993.
5. [5] R. Exel, Partial actions of groups and actions of inverse semigroups. Proc. Amer. Math. Soc. 126 (1998), 12, 3481-3494.