Consequences of shadowing property of \(G\)-spaces. (English) Zbl 1417.37063
Summary: We define and study the notion of minimality and specification for a self homeomorphism of a metric \(G\)-space \(X\). Using \(G\)-minimality, we obtain a class of maps which do not have the \(G\)-shadowing property. Further, we obtain a sufficient condition for \(G\)-expansive homeomorphisms with \(G\)-shadowing property to have \(G\)-specification property.
MSC:
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
| 54H20 | Topological dynamics (MSC2010) |
