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Title: Nekhoroshev stability for the Dirichlet Toda lattice
Authors : Henrici, Andreas
Published in : Symmetry
Volume(Issue) : 10
Issue : 10
Pages : 506
Publisher / Ed. Institution : MDPI
Issue Date: 2018
License (according to publishing contract) : CC BY 4.0: Attribution 4.0 International
Type of review: Peer review (publication)
Language : English
Subject (DDC) : 500: Natural sciences and mathematics
Abstract: In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodic Toda lattice. Precisely, by treating the phase space of the former system as an invariant subset of the latter one, namely as the fixed point set of an important symmetry of the periodic lattice, the results already obtained for the periodic lattice can be used to obtain analogous results for the Dirichlet lattice. In this way, we transfer our stability results for the periodic lattice to the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of related theorems, and the lattice with fixed ends is more important for applications than the periodic one.
Departement: School of Engineering
Organisational Unit: Institute of Applied Mathematics and Physics (IAMP)
Publication type: Article in scientific journal
DOI : 10.21256/zhaw-5042
ISSN: 2073-8994
Appears in Collections:Publikationen School of Engineering

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