Arnol′d diffusion in a pendulum lattice

V. Kaloshin, M. Levi, M. Saprykina, Communications on Pure and Applied Mathematics 67 (2014) 748–775.

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Journal Article | Published | English
Author
Kaloshin, VadimIST Austria; Levi, Mark; Saprykina, Maria
Abstract
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.
Publishing Year
Date Published
2014-05-01
Journal Title
Communications on Pure and Applied Mathematics
Volume
67
Issue
5
Page
748-775
ISSN
IST-REx-ID

Cite this

Kaloshin V, Levi M, Saprykina M. Arnol′d diffusion in a pendulum lattice. Communications on Pure and Applied Mathematics. 2014;67(5):748-775. doi:10.1002/cpa.21509
Kaloshin, V., Levi, M., & Saprykina, M. (2014). Arnol′d diffusion in a pendulum lattice. Communications on Pure and Applied Mathematics, 67(5), 748–775. https://doi.org/10.1002/cpa.21509
Kaloshin, Vadim, Mark Levi, and Maria Saprykina. “Arnol′d Diffusion in a Pendulum Lattice.” Communications on Pure and Applied Mathematics 67, no. 5 (2014): 748–75. https://doi.org/10.1002/cpa.21509.
V. Kaloshin, M. Levi, and M. Saprykina, “Arnol′d diffusion in a pendulum lattice,” Communications on Pure and Applied Mathematics, vol. 67, no. 5, pp. 748–775, 2014.
Kaloshin V, Levi M, Saprykina M. 2014. Arnol′d diffusion in a pendulum lattice. Communications on Pure and Applied Mathematics. 67(5), 748–775.
Kaloshin, Vadim, et al. “Arnol′d Diffusion in a Pendulum Lattice.” Communications on Pure and Applied Mathematics, vol. 67, no. 5, Wiley, 2014, pp. 748–75, doi:10.1002/cpa.21509.

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