Geodesic
Minimal Sets in Almost Equicontinuous Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 297-304

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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. 
@article{TM_2004_244_a11,
     author = {W. Huang and Xiangdong Ye},
     title = {Minimal {Sets} in {Almost} {Equicontinuous} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {297--304},
     publisher = {mathdoc},
     volume = {244},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_244_a11/}
}
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W. Huang; Xiangdong Ye. Minimal Sets in Almost Equicontinuous Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 297-304. http://geodesic.mathdoc.fr/item/TM_2004_244_a11/