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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

An example of Arnold diffusion for near-integrable Hamiltonians


Authors: Vadim Kaloshin and Mark Levi
Journal: Bull. Amer. Math. Soc. 45 (2008), 409-427
MSC (2000): Primary 70H08
Published electronically: April 9, 2008
MathSciNet review: 2402948
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Abstract: 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

Vadim Kaloshin
Affiliation: Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Email: kaloshin@math.psu.edu

Mark Levi
Affiliation: Mathematics 253-37, California Institute of Technology, Pasadena, California 91125

DOI: http://dx.doi.org/10.1090/S0273-0979-08-01211-1
PII: S 0273-0979(08)01211-1
Received by editor(s): March 3, 2007
Received by editor(s) in revised form: September 17, 2007
Published electronically: April 9, 2008
Additional Notes: 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
Article copyright: © Copyright 2008 American Mathematical Society