NDLI: Chaotic orbits by Melnikov's method: A survey of applications

Content Provider	IEEE Xplore Digital Library
Author	Marsden, J.E.
Copyright Year	1983
Description	Author affiliation: University of California, Berkeley (Marsden, J.E.)
Abstract	Melnikov [1963] introduced a method for proving the existence of chaotic orbits in dynamlcal systems. This was used by Arnold [1964], the paper in which "Arnold diffusion" was discovered. The method lay relatively dormant until it was revived by Chirikov [1979], Holmes [1980], and Chow, et al. [19801. In this lecture I will survey a number of recent applications of Melnikov's method to a variety of interesting physical situations. There are many modifications of the basic technique possible depending on the dimension of the system, whether or not dissipation or forcing are included or whether or not the system is autonomous. However to get the basic idea, it is useful to begin with a conservative but externally forced one degree of freedom Hamiltonian system. After presenting the basic theorem for this case in section 2, we shall discuss the generalizations of the theory in section 3 and the various applications in section 4. For additional background and applications, see Lichtenberg and Lieberman [1983] and Guckenheimer and Holmes [1983]
Starting Page	356
Ending Page	359
File Size	288189
Page Count	4
File Format	PDF
DOI	10.1109/CDC.1983.269859
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1983-12-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Chaos Orbits
Content Type	Text
Resource Type	Article

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