Results 21 to 30 of about 1,534 (98)
Fractional Perimeters from a Fractal Perspective
Advanced Nonlinear Studies, 2019 The purpose of this paper consists in a better understanding of the fractional nature of the nonlocal perimeters introduced in [L. Caffarelli, J.-M. Roquejoffre and O. Savin, Nonlocal minimal surfaces, Comm. Pure Appl. Math.
Lombardini Luca
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Isoperimetric and Poincaré Inequalities on Non-Self-Similar Sierpiński Sponges: the Borderline Case
Analysis and Geometry in Metric Spaces, 2022 In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved domains, or more ...
Eriksson-Bique Sylvester, Gong Jasun
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Box dimension, oscillation and smoothness in function spaces
Journal of Function Spaces, Volume 3, Issue 3, Page 287-320, 2005., 2005 The aim of this paper is twofold. First we relate upper and lower box dimensions with oscillation spaces, and we develop embeddings or inclusions between oscillation spaces and Besov spaces. Secondly, given a point in the (1p, s)‐plane we determine maximal and minimal values for the upper box dimension (also the maximal value for lower box dimension ...
Abel Carvalho, Hans Triebel
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Fractal and fractional dynamics for a 3D autonomous and two-wing smooth chaotic system
Alexandria Engineering Journal, 2020 Some existing chaotic systems cannot display dynamics with attractors showing a fractal representation. This is due, not only to the nature of the phenomenon under description, but also to the type of derivative operator used to express the whole model ...
Emile F. Doungmo Goufo
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Classifying Cantor Sets by their Fractal Dimensions [PDF]
, 2010 In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this
Cabrelli, Carlos A. +2 more
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Another extension of Orlicz‐Sobolev spaces to metric spaces
Abstract and Applied Analysis, Volume 2004, Issue 1, Page 1-26, 2004., 2004 We propose another extension of Orlicz‐Sobolev spaces to metric spaces based on the concepts of the Φ‐modulus and Φ‐capacity. The resulting space NΦ1 is a Banach space. The relationship between NΦ1 and MΦ1 (the first extension defined in Aïssaoui (2002)) is studied.
Noureddine Aïssaoui
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Hölder Parameterization of Iterated Function Systems and a Self-Affine Phenomenon
Analysis and Geometry in Metric Spaces, 2021 We investigate the Hölder geometry of curves generated by iterated function systems (IFS) in a complete metric space. A theorem of Hata from 1985 asserts that every connected attractor of an IFS is locally connected and path-connected.
Badger Matthew, Vellis Vyron
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Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts
, 2007 We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\mathcal B$), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1 ...
A. Zdunik +4 more
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Self‐similar random fractal measures using contraction method in probabilistic metric spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 52, Page 3299-3313, 2003., 2003 Self‐similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self‐similar
József Kolumbán +2 more
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Monoids, their boundaries, fractals and C*-algebras
Topological Algebra and its Applications, 2020 In this note we establish some connections between the theory of self-similar fractals in the sense of John E. Hutchinson (cf. [3]), and the theory of boundary quotients of C*-algebras associated to monoids.
dal Verme Giulia, Weigel Thomas
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