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Integrability and attractors

Authors
Journal
Chaos Solitons & Fractals
0960-0779
Publisher
Elsevier
Publication Date
Volume
4
Issue
11
Identifiers
DOI: 10.1016/0960-0779(94)90116-3
Disciplines
  • Mathematics

Abstract

Abstract We discuss global and local integrability and also attractors from a physicist's standpoint. A local Lie method is used to form an analytic and geometric picture of integrability via conservation laws. The starting point is Lie's proof that two-dimensional flows, even dissipative ones, have a conservation law and so are integrable. Through conservation laws, integrable higher-dimensional flows reduce to the two-dimensional case. We consider a class of models defined by the Euler-Lagrange equations for a set of nonintegrable velocities (nonholonomic coordinates). The destruction of the global conservation laws of this conservative system by the inclusion of linear damping and constant external driving leads to self-confinement and attractors in phase space. In particular, the Lorenz model belongs to this class and can be seen as a damped, driven symmetric top.

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