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This article is cited in 2 scientific papers (total in 2 papers)
On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems
Manuele Santoprete Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada
Abstract:
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.
Keywords:
bi-Hamiltonian systems; Lagrangian foliation; bott connection; symplectic connections.
Received: June 30, 2015; in final form November 3, 2015; Published online November 7, 2015
Citation:
Manuele Santoprete, “On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems”, SIGMA, 11 (2015), 089, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1070 https://www.mathnet.ru/eng/sigma/v11/p89
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Abstract page: | 132 | Full-text PDF : | 22 | References: | 20 |
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