Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Université Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
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e-mail: sebastien.neukirch (-atat-) upmc.fr

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Shape of attractors for three-dimensional dissipative dynamical systems

Sébastien Neukirch & Hector Giacomini

Physical Review E 61 #5 (2000) 5098

Abstract : We introduce a new method to bound attractors of dissipative dynamical systems in phase and parameters spaces. The method is based on the determination of families of transversal surfaces (surfaces crossed by the flow in only one direction). This technique yields very restrictive geometric bounds in phase space for the attractors. It also gives ranges of parameters of the system for which no chaotic behaviour is possible. We illustrate our method on different 3-D dissipative systems.

PACS numbers : 05.45.-a / 05.45.ac / 02.30.Hq

Key words : chaotic attractor, Lyapunov function, geometrical bounds.

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