Arnold diffusion in a pendulum lattice
Vadim Kaloshin, Mark Levi, Marya Saprykina
TL;DR
This paper investigates energy transfer in a lattice of coupled pendula, proving the existence of Arnold diffusion and estimating the rate of energy transfer for specific localized couplings.
Contribution
It provides a rigorous proof of Arnold diffusion in a pendulum lattice with localized coupling, including estimates of the energy transfer speed.
Findings
Existence of energy transfer in the lattice
Quantitative estimates of transfer speed
Proof of Arnold diffusion in the model
Abstract
The main model studied in this paper is a lattice of nearest neighbors coupled pendula. For certain localized coupling we prove existence of energy transfer and estimate its speed.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation · Opinion Dynamics and Social Influence