An example of Arnold diffusion for near-integrable Hamiltonians

Vadim Kaloshin, Mark Levi

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)409-427
Number of pages19
JournalBulletin of the American Mathematical Society
Volume45
Issue number3
DOIs
StatePublished - Jul 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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