Arnol'd diffusion in a pendulum lattice

Vadim Kaloshin, Mark Levi, Maria Saprykina

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The main model studied in this paper is a lattice of pendula with a nearest-neighbor coupling. If the coupling is weak, then the system is near-integrable and KAM tori fill most of the phase space. For all KAM trajectories the energy of each pendulum stays within a narrow band for all time. Still, we show that for an arbitrarily weak coupling of a certain localized type, the neighboring pendula can exchange energy. In fact, the energy can be transferred between the pendula in any prescribed way.

Original languageEnglish (US)
Pages (from-to)748-775
Number of pages28
JournalCommunications on Pure and Applied Mathematics
Issue number5
StatePublished - May 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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