All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 71 Next

Displaying 1401 – 1420 of 3925

Showing per page

Homeomorphisms of fractafolds

Ying Ying Chan, Robert S. Strichartz (2010)

Fundamenta Mathematicae

We classify all homeomorphisms of the double cover of the Sierpiński gasket in n dimensions. We show that there is a unique homeomorphism mapping any cell to any other cell with prescribed mapping of boundary points, and any homeomorphism is either a permutation of a finite number of topological cells or a mapping of infinite order with one or two fixed points. In contrast we show that any compact fractafold based on the level-3 Sierpiński gasket is topologically rigid.

Homogeneity and non-coincidence of Hausdorff and box dimensions for subsets of ℝⁿ

Anders Nilsson, Peter Wingren (2007)

Studia Mathematica

A class of subsets of ℝⁿ is constructed that have certain homogeneity and non-coincidence properties with respect to Hausdorff and box dimensions. For each triple (r,s,t) of numbers in the interval (0,n] with r < s < t, a compact set K is constructed so that for any non-empty subset U relatively open in K, we have ( d i m H ( U ) , d i m ̲ B ( U ) , d i m ¯ B ( U ) ) = ( r , s , t ) . Moreover, 2 - n ≤ H r ( K ) ≤ 2 n r / 2 .

Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

Jarosław Kwapisz (2001)

Fundamenta Mathematicae

We describe the homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological entropy and that they are actually semi-conjugate to an algebraic homeomorphism in the case when the entropy is positive.

Hopf's ratio ergodic theorem by inducing

Roland Zweimüller (2004)

Colloquium Mathematicae

We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.

How smooth is almost every function in a Sobolev space?

Aurélia Fraysse, Stéphane Jaffard (2006)

Revista Matemática Iberoamericana

We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.

How subadditive are subadditive capacities?

George L. O'Brien, Wim Vervaat (1994)

Commentationes Mathematicae Universitatis Carolinae

Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic sets).

Ideal convergence and divergence of nets in ( ℓ ) -groups

Antonio Boccuto, Xenofon Dimitriou, Nikolaos Papanastassiou (2012)

Czechoslovak Mathematical Journal

In this paper we introduce the ℐ - and ℐ * -convergence and divergence of nets in ( ℓ ) -groups. We prove some theorems relating different types of convergence/divergence for nets in ( ℓ ) -group setting, in relation with ideals. We consider both order and ( D ) -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that ℐ * -convergence/divergence implies ℐ -convergence/divergence for every ideal, admissible for...

Ideal limits of sequences of continuous functions

Miklós Laczkovich, Ireneusz Recław (2009)

Fundamenta Mathematicae

We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on a Polish space are of Baire class one if and only if the ideal does not contain a copy of Fin × Fin. In particular, this is true for F σ δ ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.

Idempotent States and the Inner Linearity Property

Teodor Banica, Uwe Franz, Adam Skalski (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(ℂ) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A' must be the convolution Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.

Identification of periodic and cyclic fractional stable motions

Vladas Pipiras, Murad S. Taqqu (2008)

Annales de l'I.H.P. Probabilités et statistiques

We consider an important subclass of self-similar, non-gaussian stable processes with stationary increments known as self-similar stable mixed moving averages. As previously shown by the authors, following the seminal approach of Jan Rosiński, these processes can be related to nonsingular flows through their minimal representations. Different types of flows give rise to different classes of self-similar mixed moving averages, and to corresponding general decompositions of these processes. Self-similar...

If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard

Christopher Hoffman, Daniel Rudolph (2003)

Studia Mathematica

For any 1-1 measure preserving map T of a probability space we can form the [T,Id] and [ T , T - 1 ] automorphisms as well as the corresponding endomorphisms and decreasing sequence of σ-algebras. In this paper we show that if T has zero entropy and the [T,Id] automorphism is isomorphic to a Bernoulli shift then the decreasing sequence of σ-algebras generated by the [T,Id] endomorphism is standard. We also show that if T has zero entropy and the [T²,Id] automorphism is isomorphic to a Bernoulli shift then the...

Currently displaying 1401 – 1420 of 3925