Infinite Iterated Function Systems

DOI10.1002/mana.19941700107zbMath0817.28006OpenAlexW2090388686MaRDI QIDQ4321250

Henning Fernau

Publication date: 2 February 1995

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19941700107

zbMATH Keywords

Hausdorff dimensionfractalsiterated function systemsHausdorff distanceself-similar set

Mathematics Subject Classification ID

Topological dynamics (37B99) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (28)

Hausdorff dimension of the arithmetic sum of self-similar sets ⋮ Valuations, regular expressions, and fractal geometry ⋮ The simplest erasing substitution ⋮ Hausdorff measure of infinitely generated self-similar sets ⋮ Generalized \(F\)-iterated function systems on product of metric spaces ⋮ Random iteration for infinite nonexpansive iterated function systems ⋮ The existence of the attractor of countable iterated function systems ⋮ Representations of real numbers induced by probability distributions on \(\mathbb{N}\) ⋮ Direct and inverse computation of Jacobi matrices of infinite iterated function systems ⋮ Generalized iterated function systems with place dependent probabilities ⋮ On the Hausdorff dimension of fractals given by certain expansions of real numbers ⋮ Geometric series with randomly increasing exponents ⋮ Invariant measure associated with a generalized countable iterated function system ⋮ Valuations of languages, with applications to fractal geometry ⋮ Operators on spaces of functions and measures. Vector invariant (fractal) measures ⋮ Alternative characterization of hyperbolic affine infinite iterated function systems ⋮ Generalized iterated function systems on the space \(l^\infty(X)\) ⋮ Infinite iterated function systems with overlaps ⋮ Contractive iterated function systems enriched with nonexpansive maps ⋮ A countable fractal interpolation scheme involving Rakotch contractions ⋮ Dimensions in infinite iterated function systems consisting of bi-Lipschitz mappings ⋮ On hyperbolic affine generalized infinite iterated function systems ⋮ Cyclic iterated function systems ⋮ Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements ⋮ Iterated function systems and control languages ⋮ Existence of a fractal of iterated function systems containing condensing functions for the degree of nondensifiability ⋮ Invariant (fractal) vector measures as fixed points of Markov-type operators ⋮ Thermodynamic formalism for general iterated function systems with measures

Cites Work

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• On some properties of set-dynamical systems
• Adherences of languages
• Random Recursive Constructions: Asymptotic Geometric and Topological Properties
• Self-Similar Sets. I. Topological MARKOV Chains and Mixed Self-Similar Sets

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