Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems
Інший ID:
2010 Mathematics Subject Classification: 70H06; 70G45; 37K10
DOI:10.3842/SIGMA.2015.089
DOI:10.3842/SIGMA.2015.089
Посилання:
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems / M. Santoprete // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 15 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour
of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html.
We would like to thank one of the anonymous reviewers for suggesting to us that Theorem 2
can be proved by using the uniqueness of the connection parallelizing all the Hamiltonian vector
fields tangent to the leaves of a Lagrangian foliation. This work was supported by an NSERC
Discovery Grant.
Дата:
2015
Переглядів:
491
Завантажень:
234
Анотація:
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.
