Sum of Cantor sets: Self-similarity and measure-Reference-Cited by-同舟云学术

Sum of Cantor sets: Self-similarity and measure

Published:1999-05-13 Issue:11 Volume:127 Page:3305-3308
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Mendes Pedro

Abstract

In this note it is shown that the sum of two homogeneous Cantor sets is often a uniformly contracting self-similar set and it is given a sufficient condition for such a set to be of Lebesgue measure zero (in fact, of Hausdorff dimension less than one and positive Hausdorff measure at this dimension).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1999-127-11/S0002-9939-99-05107-2/S0002-9939-99-05107-2.pdf

Reference9 articles.

1. Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure;Bandt, Christoph;Proc. Amer. Math. Soc.,1992

2. Fractals and self-similarity;Hutchinson, John E.;Indiana Univ. Math. J.,1981

3. On the topological structure of the arithmetic sum of two Cantor sets;Mendes, Pedro;Nonlinearity,1994

4. C. G. T. de A. Moreira, Stable intersections of Cantor sets and homoclinic bifurcations, Ann. Inst. Henri Poincaré: Analyse non linéaire 13 (1996), 741 – 781.

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the Structure of Arithmetic Sums of Cantor Sets Associated with Series;Results in Mathematics;2022-11-12

2. Topological structure of the sum of two homogeneous Cantor sets;Ergodic Theory and Dynamical Systems;2022-03-24

3. Cantor Set as a Fractal and Its Application in Detecting Chaotic Nature of Piecewise Linear Maps;Proceedings of the National Academy of Sciences, India Section A: Physical Sciences;2019-06-08

4. Stable intersection of affine Cantor sets defined by two expanding maps;Journal of Differential Equations;2019-02

5. On the arithmetic difference of middle Cantor sets;Discrete & Continuous Dynamical Systems - A;2018