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An example of Arnold diffusion for near-integrable Hamiltonians

Kaloshin, Vadim and Levi, Mark (2008) An example of Arnold diffusion for near-integrable Hamiltonians. Bulletin of the American Mathematical Society, 45 (3). pp. 409-427. ISSN 0273-0979.

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In this paper, using the ideas of Bessi and Mather, we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary finite change of direction for nearly constant index of refraction.

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Additional Information:© 2008 American Mathematical Society. Received by the editors March 3, 2007, and, in revised form, September 17, 2007. Article electronically published on April 9, 2008. The first author was partially supported by the Sloan Foundation and NSF grants, DMS-0701271. The second author was partially supported by NSF grant DMS-0605878.
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Sloan FoundationUNSPECIFIED
Subject Keywords:systems; orbits
Issue or Number:3
Record Number:CaltechAUTHORS:KALbams08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13561
Deposited By: Tony Diaz
Deposited On:08 May 2009 20:53
Last Modified:03 Oct 2019 00:40

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