Box-Counting Dimension Without Boxes: Computing D₀ from Average Expansion Rates

Paul So, Ernest Barreto, and Brian R. Hunt

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

Online abstract and download information

We propose an efficent 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 non-hyperbolic map.

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