Displaying similar documents to “Noninvertible minimal maps”

Uniqueness of minimal projections onto two-dimensional subspaces

Boris Shekhtman, Lesław Skrzypek (2005)

Studia Mathematica

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We prove that minimal projections from L p (1 < p < ∞) onto any two-dimensional subspace are unique. This result complements the theorems of W. Odyniec ([OL, Theorem I.1.3], [O3]). We also investigate the minimal number of norming points for such projections.

Cylinder cocycle extensions of minimal rotations on monothetic groups

Mieczysław K. Mentzen, Artur Siemaszko (2004)

Colloquium Mathematicae

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The main results of this paper are: 1. No topologically transitive cocycle ℝ m -extension of minimal rotation on the unit circle by a continuous real-valued bounded variation ℤ-cocycle admits minimal subsets. 2. A minimal rotation on a compact metric monothetic group does not admit a topologically transitive real-valued cocycle if and only if the group is finite.

Forcing relation on minimal interval patterns

Jozef Bobok (2001)

Fundamenta Mathematicae

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Let ℳ be the set of pairs (T,g) such that T ⊂ ℝ is compact, g: T → T is continuous, g is minimal on T and has a piecewise monotone extension to convT. Two pairs (T,g),(S,f) from ℳ are equivalent if the map h: orb(minT,g) → orb(minS,f) defined for each m ∈ ℕ₀ by h ( g m ( m i n T ) ) = f m ( m i n S ) is increasing on orb(minT,g). An equivalence class of this relation-a minimal (oriented) pattern A-is exhibited by a continuous interval map f:I → I if there is a set T ⊂ I such that (T,f|T) = (T,f) ∈ A. We define the forcing...

Induced subsystems associated to a Cantor minimal system

Heidi Dahl, Mats Molberg (2009)

Colloquium Mathematicae

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Let (X,T) be a Cantor minimal system and let (R,) be the associated étale equivalence relation (the orbit equivalence relation). We show that for an arbitrary Cantor minimal system (Y,S) there exists a closed subset Z of X such that (Y,S) is conjugate to the subsystem (Z,T̃), where T̃ is the induced map on Z from T. We explore when we may choose Z to be a T-regular and/or a T-thin set, and we relate T-regularity of a set to R-étaleness. The latter concept plays an important role in the...

C 1 -minimal subsets of the circle

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 C 1 -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.

Two commuting maps without common minimal points

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...

A note on universal minimal dynamical systems

Sławomir Turek (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let M ( G ) denote the phase space of the universal minimal dynamical system for a group G . Our aim is to show that M ( G ) is homeomorphic to the absolute of D 2 ω , whenever G is a countable Abelian group.

Constants of strong uniqueness of minimal norm-one projections

A. Micek (2011)

Banach Center Publications

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In this paper we calculate the constants of strong uniqueness of minimal norm-one projections on subspaces of codimension k in the space l ∞ ( n ) . This generalizes a main result of W. Odyniec and M. P. Prophet [J. Approx. Theory 145 (2007), 111-121]. We applied in our proof Kolmogorov’s type theorem (see A. Wójcik [Approximation and Function Spaces (Gdańsk, 1979), PWN, Warszawa / North-Holland, Amsterdam, 1981, 854-866]) for strongly unique best approximation.

Codimension one minimal projections in Banach spaces and a mathematical programming problem

Vladimir P. Odinec

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CONTENTSIntroduction.........................................................................................................5§1. Notation and preliminaries............................................................................6§2. Mathematical Programming Problem related to minimal projections.............8§3. Criteria for uniqueness of minimal projections in l 1 m ..........................16References......................................................................................................27 ...

Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)

Acta Arithmetica

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Density of Morse functions on sets definable in o-minimal structures

Ta Lê Loi (2006)

Annales Polonici Mathematici

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We present a tameness property of sets definable in o-minimal structures by showing that Morse functions on a definable closed set form a dense and open subset in the space of definable C p functions endowed with the Whitney topology.