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Phys. Rev. E 60, 378 - 385 (1999)

Box-counting dimension without boxes: Computing D0 from average expansion rates

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Paul So1, Ernest Barreto1, and Brian R. Hunt2
1Department of Physics and Astronomy and the Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030
2Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742

Received 20 October 1998; revised 16 February 1999

We propose an efficient iterative scheme for calculating the box-counting (capacity) dimension of a chaotic attractor in terms of its average expansion rates. Similar to the Kaplan-Yorke conjecture for the information dimension, this scheme provides a connection between a geometric property of a strange set and its underlying dynamical properties. Our conjecture is demonstrated analytically with an exactly solvable two-dimensional hyperbolic map, and numerically with a more complicated higher-dimensional nonhyperbolic map.


©1999 The American Physical Society

URL: http://link.aps.org/abstract/PRE/v60/p378
DOI: 10.1103/PhysRevE.60.378
PACS: 05.45.Df, 47.53.+n, 87.10.+e

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