On the minimal overlap problem of Erdös
L Moser (1959)
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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H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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Khalil, R. (2002)
Rendiconti del Seminario Matematico
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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.
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...
Ferry Kwakkel (2011)
Fundamenta Mathematicae
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Pierre Michel (1975)
Publications mathématiques et informatique de Rennes
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Aikawa, Hiroaki (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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S. Yamada (1987)
Inventiones mathematicae
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Ferry Kwakkel (2011)
Fundamenta Mathematicae
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As was known to H. Poincaré, an orientation preserving circle homeomorphism without periodic points is either minimal or has no dense orbits, and every orbit accumulates on the unique minimal set. In the first case the minimal set is the circle, in the latter case a Cantor set. In this paper we study a two-dimensional analogue of this classical result: we classify the minimal sets of non-resonant torus homeomorphisms, that is, torus homeomorphisms isotopic to the identity for which the...
Slavik Jablan, Ljiljana Radović, Radmila Sazdanović (2010)
Publications de l'Institut Mathématique
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