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Arnol′d Diffusion in a Pendulum Lattice
Author(s) -
Kaloshin Vadim,
Levi Mark,
Saprykina Maria
Publication year - 2014
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21509
Subject(s) - torus , phase space , integrable system , coupling (piping) , lattice (music) , pendulum , mathematics , classical mechanics , physics , mathematical analysis , geometry , quantum mechanics , materials science , acoustics , metallurgy
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. © 2014 Wiley Periodicals, Inc.