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Bulletin of the American Mathematical Society

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ISSN 1088-9485 (online) ISSN 0273-0979 (print)

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An example of Arnold diffusion for near-integrable Hamiltonians
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by Vadim Kaloshin and Mark Levi PDF
Bull. Amer. Math. Soc. 45 (2008), 409-427 Request permission


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
  • MR Author ID: 624885
  • Email:
  • Mark Levi
  • Affiliation: Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 45 (2008), 409-427
  • MSC (2000): Primary 70H08
  • DOI:
  • MathSciNet review: 2402948