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Results on normal forms for FPU chains


Henrici, A; Kappeler, T (2008). Results on normal forms for FPU chains. Communications in Mathematical Physics, 278(1):145-177.

Abstract

In this paper we prove, among other results, that near the equilibirum position, any periodic FPU chain with an odd number N of particles admits a Birkhoff normal form up to order 4, whereas any periodic FPU chain with N even admits a resonant normal form up to order 4. This resonant normal form of order 4 turns out to be completely integrable. Further, for N odd, we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point.

Abstract

In this paper we prove, among other results, that near the equilibirum position, any periodic FPU chain with an odd number N of particles admits a Birkhoff normal form up to order 4, whereas any periodic FPU chain with N even admits a resonant normal form up to order 4. This resonant normal form of order 4 turns out to be completely integrable. Further, for N odd, we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point.

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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:February 2008
Deposited On:14 Jan 2009 14:04
Last Modified:18 Feb 2018 10:01
Publisher:Springer
ISSN:0010-3616
Additional Information:The original publication is available at www.springerlink.com
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s00220-007-0387-z
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2367202

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