ON THE MENDÈS FRANCE FRACTAL DIMENSION OF STRANGE ATTRACTORS: THE HÉNON CASE-Reference-Cited by-同舟云学术

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

Published:2002-07 Issue:07 Volume:12 Page:1549-1563
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

PIACQUADIO M.¹,HANSEN R.¹,PONTA F.¹²

Affiliation:

1. Dpto. de Matemática, Fac. de Ingeniería, Universidad de Buenos Aires, Av. Paseo Colón 850, (1063) Buenos Aires, Argentina

2. ISEP Group, Dpto. de Electrotecnia, Fac. de Ingeniería, Universidad de Buenos Aires, Av. Paseo Colón 850, (1063) Buenos Aires, Argentina

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127402005285

Reference3 articles.

1. The Planck constant of a curve

2. Chaos and Fractals

3. Curves and Fractal Dimension

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