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Displaying similar documents to “On the classification of inverse limits of tent maps”

Induced mappings on hyperspaces F n K ( X )

Enrique Castañeda-Alvarado, Roberto C. Mondragón-Alvarez, Norberto Ordoñez (2024)

Commentationes Mathematicae Universitatis Carolinae

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Given a metric continuum X and a positive integer n , F n ( X ) denotes the hyperspace of all nonempty subsets of X with at most n points endowed with the Hausdorff metric. For K F n ( X ) , F n ( K , X ) denotes the set of elements of F n ( X ) containing K and F n K ( X ) denotes the quotient space obtained from F n ( X ) by shrinking F n ( K , X ) to one point set. Given a map f : X Y between continua, f n : F n ( X ) F n ( Y ) denotes the induced map defined by f n ( A ) = f ( A ) . Let K F n ( X ) , we shall consider the induced map in the natural way f n , K : F n K ( X ) F n f ( K ) ( Y ) . In this paper we consider the maps f , f n , f n , K for some...

Finite-dimensional maps and dendrites with dense sets of end points

Hisao Kato, Eiichi Matsuhashi (2006)

Colloquium Mathematicae

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The first author has recently proved that if f: X → Y is a k-dimensional map between compacta and Y is p-dimensional (0 ≤ k, p < ∞), then for each 0 ≤ i ≤ p + k, the set of maps g in the space C ( X , I p + 2 k + 1 - i ) such that the diagonal product f × g : X Y × I p + 2 k + 1 - i is an (i+1)-to-1 map is a dense G δ -subset of C ( X , I p + 2 k + 1 - i ) . In this paper, we prove that if f: X → Y is as above and D j (j = 1,..., k) are superdendrites, then the set of maps h in C ( X , j = 1 k D j × I p + 1 - i ) such that f × h : X Y × ( j = 1 k D j × I p + 1 - i ) is (i+1)-to-1 is a dense G δ -subset of C ( X , j = 1 k D j × I p + 1 - i ) for each 0 ≤ i ≤ p.

Weighted w -core inverses in rings

Liyun Wu, Huihui Zhu (2023)

Czechoslovak Mathematical Journal

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Let R be a unital * -ring. For any a , s , t , v , w R we define the weighted w -core inverse and the weighted dual s -core inverse, extending the w -core inverse and the dual s -core inverse, respectively. An element a R has a weighted w -core inverse with the weight v if there exists some x R such that a w x v x = x , x v a w a = a and ( a w x ) * = a w x . Dually, an element a R has a weighted dual s -core inverse with the weight t if there exists some y R such that y t y s a = y , a s a t y = a and ( y s a ) * = y s a . Several characterizations of weighted w -core invertible and weighted dual s -core...

On affinity of Peano type functions

Tomasz Słonka (2012)

Colloquium Mathematicae

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We show that if n is a positive integer and 2 , then for every positive integer m and for every real constant c > 0 there are functions f , . . . , f n + m : such that ( f , . . . , f n + m ) ( ) = n + m and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that ( f i , . . . , f i ) ( y ) = y + w for y x + ( - c , c ) × n - 1 .

Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps

Viviane Baladi, Daniel Smania (2012)

Annales scientifiques de l'École Normale Supérieure

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We consider C 2 families t f t of  C 4 unimodal maps f t whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure μ t of  f t depends differentiably on  t , as a distribution of order 1 . The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of  μ t for a Benedicks-Carleson map f t , in terms of a single smooth function and the...

Linear maps preserving A -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

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Let be a complex Hilbert space, A a positive operator with closed range in ( ) and A ( ) the sub-algebra of ( ) of all A -self-adjoint operators. Assume φ : A ( ) onto itself is a linear continuous map. This paper shows that if φ preserves A -unitary operators such that φ ( I ) = P then ψ defined by ψ ( T ) = P φ ( P T ) is a homomorphism or an anti-homomorphism and ψ ( T ) = ψ ( T ) for all T A ( ) , where P = A + A and A + is the Moore-Penrose inverse of A . A similar result is also true if φ preserves A -quasi-unitary operators in both directions such that there...

Cobham's theorem for substitutions

Fabien Durand (2011)

Journal of the European Mathematical Society

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The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then a sequence x A , where A is a finite alphabet, is both α -substitutive and β -substitutive if and only if x is ultimately...

A compactness result for polyharmonic maps in the critical dimension

Shenzhou Zheng (2016)

Czechoslovak Mathematical Journal

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For n = 2 m 4 , let Ω n be a bounded smooth domain and 𝒩 L a compact smooth Riemannian manifold without boundary. Suppose that { u k } W m , 2 ( Ω , 𝒩 ) is a sequence of weak solutions in the critical dimension to the perturbed m -polyharmonic maps d d t | t = 0 E m ( Π ( u + t ξ ) ) = 0 with Φ k 0 in ( W m , 2 ( Ω , 𝒩 ) ) * and u k u weakly in W m , 2 ( Ω , 𝒩 ) . Then u is an m -polyharmonic map. In particular, the space of m -polyharmonic maps is sequentially compact for the weak- W m , 2 topology.

On open maps and related functions over the Salbany compactification

Mbekezeli Nxumalo (2024)

Archivum Mathematicum

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Given a topological space X , let 𝒰 X and η X : X 𝒰 X denote, respectively, the Salbany compactification of X and the compactification map called the Salbany map of X . For every continuous function f : X Y , there is a continuous function 𝒰 f : 𝒰 X 𝒰 Y , called the Salbany lift of f , satisfying ( 𝒰 f ) η X = η Y f . If a continuous function f : X Y has a stably compact codomain Y , then there is a Salbany extension F : 𝒰 X Y of f , not necessarily unique, such that F η X = f . In this paper, we give a condition on a space such that its Salbany map is open. In...

Hardness of embedding simplicial complexes in d

Jiří Matoušek, Martin Tancer, Uli Wagner (2011)

Journal of the European Mathematical Society

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Let 𝙴𝙼𝙱𝙴𝙳 k d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k , does there exist a (piecewise linear) embedding of K into d ? Known results easily imply polynomiality of 𝙴𝙼𝙱𝙴𝙳 k 2 ( k = 1 , 2 ; the case k = 1 , d = 2 is graph planarity) and of 𝙴𝙼𝙱𝙴𝙳 k 2 k for all k 3 . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that 𝙴𝙼𝙱𝙴𝙳 d d and 𝙴𝙼𝙱𝙴𝙳 ( d - 1 ) d are undecidable for each d 5 . Our main result is NP-hardness of 𝙴𝙼𝙱𝙴𝙳 2 4 and, more generally, of 𝙴𝙼𝙱𝙴𝙳 k d for all...

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.