A PRIMER OF NEGATIVE TEST DIMENSIONS AND DEGREES OF EMPTINESS FOR LATENT SETS-Reference-Cited by-同舟云学术

A PRIMER OF NEGATIVE TEST DIMENSIONS AND DEGREES OF EMPTINESS FOR LATENT SETS

Published:2009-03 Issue:01 Volume:17 Page:1-14
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

MANDELBROT BENOIT B.¹,FRAME MICHAEL¹

Affiliation:

1. Mathematics Department, Yale University, 10 Hillhouse Ave., P. O. Box 208283, New Haven, CT, 06520-8283, USA

Abstract

Applied blindly, the formula for the dimension of the intersection can give negative results. Extending Minkowski's definition of the dimension by ∊-neighborhoods to ∊-pseudo-neighborhoods, that is, replacing (A ∩ B)∊ with A∊ ∩ B∊, we introduce the notion of negative dimensions through several examples of random fractal constructions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X09004211

Reference28 articles.

1. B. Mandelbrot, Fractals' Physical Origin and Properties, ed. L. Pietronero (Plenum, Erice, 1988) pp. 3–29.

2. B. Mandelbrot, Chaos: Soviet-American Perspectives on Nonlinear Science, ed. D. Campbell (American Institute of Physics, 1990) pp. 79–90.

3. Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism

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