The complete integrability of a Lie-Poisson system proposed by Bloch and Iserles
| dc.creator | Tomei, Carlos | |
| dc.creator | Li, Luen-Chau | |
| dc.date | 2005-12-12 | |
| dc.date.accessioned | 2026-07-07T06:55:05Z | |
| dc.date.available | 2026-07-07T06:55:05Z | |
| dc.description | We establish the Liouville integrability of the differential equation $\dot S(t)= [N,S^2(t)],$ recently considered by Bloch and Iserles. Here, $N$ is a real, fixed, skew-symmetric matrix and $S$ is real symmetric. The equation is realized as a Hamiltonian vector field on a coadjoint orbit of a loop group, and sufficiently many commuting integrals are presented, together with a solution formula for their related flows in terms of a Riemann-Hilbert factorization problem. We also answer a question raised by Bloch and Iserles, by realizing the same system on a coadjoint orbit of a finite dimensional Lie group. | |
| dc.description | 16 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0512246 | |
| dc.identifier | http://arxiv.org/abs/math/0512246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106172 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 37K10, 70H06; 35Q58, 22E67 | |
| dc.title | The complete integrability of a Lie-Poisson system proposed by Bloch and Iserles | |
| dc.type | text |