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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.

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