Henrici, A; Kappeler, T (2008). Results on normal forms for FPU chains. Communications in Mathematical Physics, 278(1):145-177.
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.
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.
| 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 > Statistical and Nonlinear Physics
Physical Sciences > Mathematical Physics |
| Language: | English |
| Date: | February 2008 |
| Deposited On: | 14 Jan 2009 14:04 |
| Last Modified: | 01 Dec 2023 02:48 |
| Publisher: | Springer |
| ISSN: | 0010-3616 |
| Additional Information: | The original publication is available at www.springerlink.com |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/s00220-007-0387-z |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2367202 |
Henrici, A