Results 21 to 30 of about 1,536 (100)
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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Function spaces on the Koch curve
Journal of Function Spaces, Volume 8, Issue 3, Page 287-299, 2010., 2010 We consider two types of Besov spaces on the Koch curve, defined by traces and with the help of the snowflaked transform. We compare these spaces and give their characterization in terms of Daubechies wavelets.
Maryia Kabanava, Hans Triebel
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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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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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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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On Lebesgue measure of integral self-affine sets
, 2011 Let $A$ be an expanding integer $n\times n$ matrix and $D$ be a finite subset of $Z^n$. The self-affine set $T=T(A,D)$ is the unique compact set satisfying the equality $A(T)=\cup_{d\in D} (T+d)$. We present an effective algorithm to compute the Lebesgue
G.-T. Deng +10 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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Moments of the weighted Cantor measures
Demonstratio Mathematica, 2019 Based on the seminal work of Hutchinson, we investigate properties of α-weighted Cantor measures whose support is a fractal contained in the unit interval.
Harding Steven N. +1 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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The "hot spots" conjecture on the Vicsek set
Demonstratio Mathematica, 2019 We prove the “hot spots” conjecture on the Vicsek set. Specifically, we will show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.
Ionescu Marius, Savage Thomas L.
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