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Title: Nekhoroshev theorem for the Dirichlet Toda chain
Authors : Henrici, Andreas
et. al : No
Conference details: Symmetry 2017, 1st International Conference on Symmetry, Barcelona, Spain, 16-18 October 2017
Publisher / Ed. Institution : ZHAW Zürcher Hochschule für Angewandte Wissenschaften
Publisher / Ed. Institution: Winterthur
Issue Date: 16-Oct-2017
License (according to publishing contract) : CC BY 4.0: Attribution 4.0 International
Type of review: Peer review (publication)
Language : English
Subjects : Integrable systems; Toda chain
Subject (DDC) : 500: Natural sciences and mathematics
Abstract: In this work, we prove a Nekhoroshev theorem for the Toda chain with Dirichlet boundary conditions, i.e., fixed ends. The Toda chain is a special case of a Fermi-Pasta-Ulam (FPU) chain, and in view of the unexpected recurrence phenomena observed numerically in these chains, it has been conjectured that theory of perturbed integrable systems could be applied to these chains, especially since the Toda chain has been shown to be a completely integrable system. Whereas various results have already been obtained for the periodic lattice, the Dirichlet chain is more important from the point of view of applications, since the famous numerical experiments have been performed for this type of system. Mathematically, the Dirichlet chain can be treated by exploiting symmetries of the periodic chain. Precisely, by considering the phase space of the Dirichlet chain as an invariant submanifold of the periodic chain, namely the fixed point set of a certain symmetry of the periodic chain, the results obtained for the periodic chain can be used to obtain similar results for the Dirichlet chain. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of other results such as those of the KAM theorem.
Departement: School of Engineering
Organisational Unit: Institute of Applied Mathematics and Physics (IAMP)
Publication type: Conference poster
DOI : 10.21256/zhaw-5533
Appears in Collections:Publikationen School of Engineering

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