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BY-NC-ND 3.0 license Open Access Published by De Gruyter June 2, 2014

A "Superfat" Attractor with a Singular-Continuous 2-D Weierstrass Function in a Cross Section

  • O. E. Rössler and J. L. Hudson

Abstract

A 3-D invertible map generating a 4-loop solenoid attractor is presented. The attractor of the "standard" 4-solenoid turns out to be "fat" - that is, fractal dimensionality exceeds topological dimensionality by more than unity. If a fourth variable that is weakly damped is added to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowhere-differentiable function over a 2-D domain which is a 2-D Cantor set. Such an object can be called a "singular-continuous 2-D Weierstrass function". The latter can be "superfat" (dimension gap larger than 2). Realistic systems possessing attractors of this new type are possible.

Received: 1992-11-27
Published Online: 2014-6-2
Published in Print: 1993-6-1

© 1946 – 2014: Verlag der Zeitschrift für Naturforschung

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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