Header

UZH-Logo

Maintenance Infos

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.

Statistics

Citations

Dimensions.ai Metrics
8 citations in Web of Science®
8 citations in Scopus®
9 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

40 downloads since deposited on 01 Feb 2010
9 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics
Language:English
Date:2009
Deposited On:01 Feb 2010 17:38
Last Modified:29 Jul 2020 21:16
Publisher:European Mathematical Society
ISSN:1435-9855
OA Status:Hybrid
Publisher DOI:https://doi.org/10.4171/JEMS/174
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

Download

Hybrid Open Access