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Resonant normal form for even periodic FPU chains


Henrici, A; Kappeler, T (2009). Resonant normal form for even periodic FPU chains. Journal of the European Mathematical Society, 11(5):1025-1056.

Abstract

We investigate periodic FPU chains with an even number of particles. We show that near the equilibrium point, any such chain admits a resonant Birkhoff normal form of order four which is completely integrable—an important fact which helps explain the numerical experiments of Fermi, Pasta, and Ulam. We analyze the moment map of the integrable approximation of an even FPU chain. Unlike the case of odd FPU chains these integrable systems (generically) exhibit hyperbolic dynamics. As an application we prove that any FPU chain with Dirichlet boundary conditions admits a Birkhoff normal form up to order four and show that a KAM theorem applies.

Abstract

We investigate periodic FPU chains with an even number of particles. We show that near the equilibrium point, any such chain admits a resonant Birkhoff normal form of order four which is completely integrable—an important fact which helps explain the numerical experiments of Fermi, Pasta, and Ulam. We analyze the moment map of the integrable approximation of an even FPU chain. Unlike the case of odd FPU chains these integrable systems (generically) exhibit hyperbolic dynamics. As an application we prove that any FPU chain with Dirichlet boundary conditions admits a Birkhoff normal form up to order four and show that a KAM theorem applies.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:01 Feb 2010 17:38
Last Modified:05 Apr 2016 13:50
Publisher:European Mathematical Society
ISSN:1435-9855
Official URL:http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=11&iss=5&rank=4
Related URLs:http://arxiv.org/abs/0709.2624

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