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Stochastic Representation of Chaos using Terminal AttractorsA nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.
Document ID
20080022187
Acquisition Source
Jet Propulsion Laboratory
Document Type
Reprint (Version printed in journal)
Authors
Zak, Michail
(Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
August 24, 2013
Publication Date
May 1, 2005
Publication Information
Publication: Chaos, Solutions and Fractals
Volume: 24
Issue: 3
Subject Category
Mathematical And Computer Sciences (General)
Distribution Limits
Public
Copyright
Other
Keywords
stochastic processes
chaos
Liouville equation
turbulence

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