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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2004 Volume 244, Pages 297–304 (Mi tm450)

This article is cited in 4 papers

Minimal Sets in Almost Equicontinuous Systems

W. Huang, Xiangdong Ye

University of Science and Technology of China

Abstract: 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.

UDC: 517.91+517.93

Received in October 2000

Language: English


 English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 244, 280–287

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