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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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.
H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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Matthieu Joseph, Tapio Rajala (2017)
Analysis and Geometry in Metric Spaces
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We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance d such that the product of snowflaked Euclidean lines looks down on (RN , d), but not vice versa.
Marie Rüdigerová (1965)
Aplikace matematiky
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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Khalil, R. (2002)
Rendiconti del Seminario Matematico
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Morris, Robert (2009)
The Electronic Journal of Combinatorics [electronic only]
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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...