Minimal Niven numbers
H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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L Moser (1959)
Acta Arithmetica
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Asit Baran-Raha (1972)
Colloquium Mathematicae
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Pierre Michel (1975)
Publications mathématiques et informatique de Rennes
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Basilio Messano, Antonio Zitarosa (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We introduce generalized dynamical systems (including both dynamical systems and discrete dynamical systems) and give the notion of minimal set of a generalized dynamical system. Then we prove a generalization of the classical G.D. Birkhoff theorem about minimal sets of a dynamical system and some propositions about generalized discrete dynamical systems.
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...
J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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Aikawa, Hiroaki (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Basilio Messano, Antonio Zitarosa (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We introduce generalized dynamical systems (including both dynamical systems and discrete dynamical systems) and give the notion of minimal set of a generalized dynamical system. Then we prove a generalization of the classical G.D. Birkhoff theorem about minimal sets of a dynamical system and some propositions about generalized discrete dynamical systems.
Jürg Schmid, Jürgen Schmidt (1987)
Colloquium Mathematicae
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Walter H. Gottschalk (1964)
Annales de l'institut Fourier
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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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.
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.