|
Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems
Manuele Santoprete Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada
Аннотация:
Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fassò and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. The second proof uses Darboux–Nijenhuis coordinates and symplectic connections.
Ключевые слова:
bi-Hamiltonian systems; Lagrangian foliation; bott connection; symplectic connections.
Поступила: 30 июня 2015 г.; в окончательном варианте 3 ноября 2015 г.; опубликована 7 ноября 2015 г.
Образец цитирования:
Manuele Santoprete, “On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems”, SIGMA, 11 (2015), 089, 11 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1070 https://www.mathnet.ru/rus/sigma/v11/p89
|
Статистика просмотров: |
Страница аннотации: | 132 | PDF полного текста: | 22 | Список литературы: | 20 |
|