Transformation groups with no equicontinuous minimal set
Jason Gait (1972)
Compositio Mathematica
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Jason Gait (1972)
Compositio Mathematica
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Asit Baran-Raha (1972)
Colloquium Mathematicae
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L Moser (1959)
Acta Arithmetica
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H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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Tomasz Downarowicz (2011)
Colloquium Mathematicae
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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...
Dusa McDuff (1981)
Annales de l'institut Fourier
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Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.
Joseph Auslander, Brindell Horelick (1970)
Compositio Mathematica
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Dariusz Tywoniuk (2012)
Colloquium Mathematicae
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We construct a continuous non-invertible minimal transformation of an arbitrary solenoid. Since solenoids, as all other compact monothetic groups, also admit minimal homeomorphisms, our result allows one to classify solenoids among continua admitting both invertible and non-invertible continuous minimal maps.
Holmes, P.E. (2004)
Experimental Mathematics
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Pierre Michel (1975)
Publications mathématiques et informatique de Rennes
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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