The capacity for a class of fractal functions

DOI10.1007/BF01205937zbMath0605.28006MaRDI QIDQ1084207

Douglas P. Hardin, Peter R. Massopust

Publication date: 1986

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

capacityLyapunov exponentsdynamical systemattractoriterated function systemfractal functions

Mathematics Subject Classification ID

Related Items (30)

FRACTAL DIMENSION OF MULTIVARIATE α-FRACTAL FUNCTIONS AND APPROXIMATION ASPECTS ⋮ Approximation of rough functions ⋮ A GENERALIZATION OF FRACTAL INTERPOLATION STOCHASTIC PROCESSES TO HIGHER DIMENSIONS ⋮ Recurrent iterated function systems ⋮ A remarkable fact for the box dimensions of fractal interpolation curves of \(\mathbb{R}^3\) ⋮ Hölder exponents and box dimension for self-affine fractal functions ⋮ Newton's method for fractal approximation ⋮ Dimension and differentiability of a class of fractal interpolation functions ⋮ BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES ⋮ Box dimension of \(\alpha\)-fractal function with variable scaling factors in subintervals ⋮ PSEUDO RANDOM NUMBER GENERATION WITH THE AID OF ITERATED FUNCTION SYSTEMS ON ℝ² ⋮ Fractal dimension for a class of complex-valued fractal interpolation functions ⋮ A very general framework for fractal interpolation functions ⋮ Dimension preserving approximation ⋮ Fractal Peano curves ⋮ Self-affine fractal functions and wavelet series ⋮ Vector-valued fractal interpolation functions and their box dimensions ⋮ Dimensional analysis of \(\alpha\)-fractal functions ⋮ Multiresolution analyses based on fractal functions ⋮ Wavelet Analysis of Self Similar Functions ⋮ Bilinear fractal interpolation and box dimension ⋮ A general construction of fractal interpolation functions on grids of ⁿ ⋮ BOX DIMENSION OF A NONLINEAR FRACTAL INTERPOLATION CURVE ⋮ Fractal surfaces ⋮ On the box-counting dimension of graphs of harmonic functions on the Sierpiński gasket ⋮ Fractal and Hausdorff dimensions for systems of iterative functional equations ⋮ Stereographic metric and dimensions of fractals on the sphere ⋮ Fractal convolution: A new operation between functions ⋮ On bivariate fractal approximation ⋮ EXISTENCE AND BOX DIMENSION OF GENERAL RECURRENT FRACTAL INTERPOLATION FUNCTIONS

Cites Work

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• The Lyapunov dimension of strange attractors
• A Mandelbrot set for pairs of linear maps
• The Lyapunov dimension of a nowhere differentiable attracting torus
• Invariant Densities for Random Maps of the Interval
• Iterated function systems and the global construction of fractals
• Sets of Fractional Dimensions (V): on Dimensional Numbers of Some Continuous Curves

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