Erratum to "Minimal sets of non-resonant torus homeomorphisms" (Fund. Math. 211 (2011), 41-76)
Ferry Kwakkel (2011)
Fundamenta Mathematicae
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Ferry Kwakkel (2011)
Fundamenta 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.
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...
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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Jason Gait (1972)
Compositio Mathematica
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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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Wojciech Hyb (1978)
Colloquium Mathematicae
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Sergiĭ Kolyada, L'ubomír Snoha, Sergeĭ Trofimchuk (2001)
Fundamenta Mathematicae
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For a discrete dynamical system given by a compact Hausdorff space X and a continuous selfmap f of X the connection between minimality, invertibility and openness of f is investigated. It is shown that any minimal map is feebly open, i.e., sends open sets to sets with nonempty interiors (and if it is open then it is a homeomorphism). Further, it is shown that if f is minimal and A ⊆ X then both f(A) and share with A those topological properties which describe how large a set is. Using...
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.
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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