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Chaos and Arnold diffusion in dynamical systems

Salam, Fathi M. A. and Marsden, Jerrold E. and Varaiya, Pravin P. (1983) Chaos and Arnold diffusion in dynamical systems. IEEE Transactions on Circuits and Systems, 30 (9). pp. 697-708. ISSN 0098-4094.

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Chaotic motion refers to complicated trajectories in dynamical systems. It occurs even in deterministic systems governed by simple differential equations and its presence has been experimentally verified for many systems in several disciplines. A technique due to Melnikov provides an analytical tool for measuring chaos caused by horseshoes in certain systems. The phenomenon of Arnold diffusion is another type of complicated behavior. Since 1964, it has been playing an important role for Hamiltonian systems in physics. We present a tutorial treatment of this work and its place in dynamical systems theory, with an emphasis on results that can be checked in specific systems. A generalization of the Melnikov technique has been recently developed to treatn-degree of freedom Hamiltonian systems whenn > 3. We extend the Melnikov technique to certain non-Hamiltonian systems of ordinary differential equations. The extension is made with a view to applications in the physical sciences and engineering.

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Additional Information:© 1983 IEEE. "Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received January 10, 1982; revised February 10, 1983. This work is supported in part by DOE under Contract DE-ASOI-78ET29135 and under Contract DE-AT03-82 ER 12097.
Issue or Number:9
Record Number:CaltechAUTHORS:SALieeetc83
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
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Deposited On:31 Oct 2005
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