Fractal Dimensions of Chaotic Saddles of Dynamical Systems

Brian R. Hunt, Edward Ott, and James A. Yorke

Phys. Rev. E 54 (1996), 4819-4823.

A formula, applicable to invertible maps of arbitrary dimensionality, is derived for the information dimensions of the natural measures of a nonattracting chaotic set and of its stable and unstable manifolds. The result gives these dimensions in terms of the Lyapunov exponents and the decay time of the associated chaotic transient. As an example, the formula is applied to the physically interesting situation of filtering of data from chaotic systems.

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