Phys. Rev. E 60, 378–385 (1999)Box-counting dimension without boxes: Computing D0 from average expansion ratesReceived 20 October 1998; revised 16 February 1999; published in the issue dated July 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/doi/10.1103/PhysRevE.60.378
DOI:
10.1103/PhysRevE.60.378
PACS:
05.45.Df, 47.53.+n, 87.10.+e
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