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

Paul So, Ernest Barreto, and Brian R. Hunt
Phys. Rev. E 60, 378 – Published 1 July 1999
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Abstract

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.

  • Received 20 October 1998

DOI:https://doi.org/10.1103/PhysRevE.60.378

©1999 American Physical Society

Authors & Affiliations

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

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Vol. 60, Iss. 1 — July 1999

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