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The equality of fractal dimension and uncertainty dimension for certain dynamical systems. (English) Zbl 0770.58030
For a one- and two-dimensional dynamical system which has finitely many but at least two attractors, and is uniformly hyperbolic on their basin boundary it is proved that box-counting dimension, uncertainty dimension and Hausdorff dimension are equal for the basin boundary.

37D99 Dynamical systems with hyperbolic behavior
28A78 Hausdorff and packing measures
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI
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