On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems
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| Creator |
Santoprete, M.
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| Description |
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.
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| Date |
2019-02-13T17:58:04Z
2019-02-13T17:58:04Z 2015 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 70H06; 70G45; 37K10 DOI:10.3842/SIGMA.2015.089 http://dspace.nbuv.gov.ua/handle/123456789/147160 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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