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

P So·E Barreto·B R Hunt
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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.

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Biophysical PhenomenaBiophysicsModels, StatisticalModels, TheoreticalNonlinear DynamicsJournal ArticleResearch Support, U.S. Gov't, Non-P.H.S.Research Support, U.S. Gov't, P.H.S.

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P So, E Barreto, B R Hunt. 1999. Box-counting dimension without boxes: computing D0 from average expansion rates.. https://doi.org/10.1103/physreve.60.378

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