Box-counting dimension without boxes: computing D0 from average expansion rates.
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.
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Department of Physics and Astronomy and the Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030, USA.
Barreto
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Hunt
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D055592:Biophysical Phenomena; D001703:Biophysics; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics