ZERAOULIA ELHADJ

Department of Mathematics,

University of T´eb´essa, (12000), Algeria

zeraoulia@mail.univ-tebessa.dz

zelhadj12@yahoo.fr

J. C. SPROTT

Department of Physics, University of Wisconsin,

Madison, WI 53706, USA

sprott@physics.wisc.edu

Received January 28, 2012; Revised July 12, 2012

There are many examples of
nonconnected chaotic attractors consisting of several
components. The determination of an overall period of such a
system is typically done only by a numerical integration of the
system. In this letter, we provide a rigorous proof that the
exact value of the overall period of a particular 2-D chaotic
attractor from an iterated map is two once the attractor has
partitioned and quantized into disconnected sets. As far as we
know, there are no examples of a rigorous proof for such a
property in the current literature.

Ref: E.
Zeraoulia and J. C. Sprott,
International Journal of Bifurcation and Chaos 23, 1350046 (2013)

The complete paper is available in
PDF format.

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Fig. 1. Attractors of the map (1) with (a)