ON THE MENDÈS FRANCE FRACTAL DIMENSION OF STRANGE ATTRACTORS: THE HÉNON CASE

Abstract

We consider the Hénon attractor ℋ as a curve limit of continuous planar curves H(n), as n → ∞. We describe a set of tools for studying the Hausdorff dimension dim H of a certain family of such curves, and we adapt these tools to the particular case of the Hénon attractor, estimating its Hausdorff dimension dim H (ℋ) to be about 1.258, a number smaller than the usual estimates for the box-counting dimension of the attractor. We interpret this discrepancy.