Dimensionality of strange attractors determined analytically
Abstract
An analytical method for determination of the dimensionality of strange attractors in two-dimensional maps is introduced. In this method, the geometric structure of an attractor is obtained from a procedure developed previously. Such structures often appear to the Cartesian product of a curve and a Cantor set. From the geometric structures, we determine the Hausdorff dimension first for the Cantor set, and then for the attractor. The results compare well with numerical results obtained for the Hénon, Zaslavskii, and Kaplan-Yorke maps.
- Publication:
-
Physical Review Letters
- Pub Date:
- September 1986
- DOI:
- 10.1103/PhysRevLett.57.1390
- Bibcode:
- 1986PhRvL..57.1390T
- Keywords:
-
- Dimensional Analysis;
- Fractals;
- Strange Attractors;
- Transformations (Mathematics);
- Analytic Functions;
- Chaos;
- Geometry;
- Manifolds (Mathematics);
- Physics (General);
- 05.45+b;
- 02.50+s;
- 03.20+i;
- 05.40+j