Dimensionality of Strange Attractors Determined Analytically

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Abstract
An analytical method to determine the dimensionality of strange attractors in two-dimensional maps is introduced. In this method, the geometric structures of an attractor are obtained from a procedure developed previously. Such structures often appear to be the Cartesian product of a curve and a Cantor set. From the geometric structures, we determine the Hausdorff dimension first for the Cantor set, and then for the attractor. The results compare well with numerical results obtained for the Hénon, Zaslavskii, and Kaplan-Yorke maps.