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**Minimal sets in almost equicontinuous systems.**
*(English)*
Zbl 1072.37012

Dynamical systems and related problems of geometry. Collected papers dedicated to the memory of Academician Andrei Andreevich Bolibrukh. Transl. from the Russian. Moscow: Maik Nauka/Interperiodika. Proceedings of the Steklov Institute of Mathematics 244, 280-287 (2004) and Tr. Mat. Inst. Steklova 244, 297-304 (2004).

Summary: Supplying necessary and sufficient conditions such that a transitive system (as a subsystem of the Bebutov system) is uniformly rigid and using the fact that each transitive uniformly rigid system has an almost equicontinuous extension, we construct almost equicontinuous systems containing \(n\), \(n\in\mathbb N\), countably many, and uncountably many minimal sets, which serve as new examples of almost equicontinuous systems. Our method is quite general as each transitive uniformly rigid system has a factor that is a subsystem of the Bebutov system. Moreover, we explore how the number of connected components in a transitive pointwise recurrent system is related to the connectedness of the minimal sets contained in the system.

For the entire collection see [Zbl 1064.37002].

For the entire collection see [Zbl 1064.37002].

### 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 |

54H20 | Topological dynamics (MSC2010) |