Generic uniqueness of a minimal solution for variational problems on a torus.
Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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Zaslavski, Alexander J. (2002)
Abstract and Applied Analysis
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Asit Baran-Raha (1972)
Colloquium Mathematicae
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L Moser (1959)
Acta Arithmetica
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Sergio Fratarcangeli (2008)
Fundamenta Mathematicae
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The purpose of this paper is to extend a theorem of Speissegger [J. Reine Angew. Math. 508 (1999)], which states that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Specifically, we display a collection of properties possessed by the real numbers that suffices for a version of the proof of this theorem to go through. The degree of flexibility revealed in this study permits the use of certain model-theoretic arguments for the first time, e.g. the compactness...
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...
Y.-C. Hsieh, T.-C. Chen (2007)
The Yugoslav Journal of Operations Research
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J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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Pierre Michel (1975)
Publications mathématiques et informatique de Rennes
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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.
Aikawa, Hiroaki (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Jürg Schmid, Jürgen Schmidt (1987)
Colloquium Mathematicae
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Krzysztof Bolibok (2014)
Studia Mathematica
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We show that every subspace of finite codimension of the space C[0,1] is extremal with respect to the minimal displacement problem.
Lou van den Dries, Jana Maříková (2010)
Fundamenta Mathematicae
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In answering questions of J. Maříková [Fund. Math. 209 (2010)] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V, and let st: V → k be the corresponding standard part map. Under a mild assumption on (R,V) we show that a definable set X ⊆ Vⁿ admits a triangulation that induces a triangulation of its standard part st X ⊆ kⁿ.
Guido De Philippis, Emanuele Paolini (2009)
Rendiconti del Seminario Matematico della Università di Padova
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