Hyper-symplectic structures on integrable systems
نویسندگان
چکیده
منابع مشابه
Semitoric integrable systems on symplectic 4-manifolds
Let (M, ω) be a symplectic 4-manifold. A semitoric integrable system on (M, ω) is a pair of smooth functions J, H ∈ C∞(M, R) for which J generates a Hamiltonian S-action and the Poisson brackets {J, H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about t...
متن کاملIntegrable Systems in Symplectic Geometry
Quaternionic vector mKDV equations are derived from the Cartan structure equation in the symmetric space n =Sp(n+ 1)/Sp(1)×Sp(n). The derivation of the soliton hierarchy utilizes a moving parallel frame and a Cartan connection 1-form ω related to the Cartan geometry on n modelled on (spn+1, sp1 × spn). The integrability structure is shown to be geometrically encoded by a Poisson– Nijenhuis stru...
متن کاملSymplectic theory of completely integrable Hamiltonian systems
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of singular affine structures. These developments make use of results obtained by many authors in the second half of the twentieth century, notably Arnold, Duisterm...
متن کاملExamples of Integrable and Non-integrable Systems on Singular Symplectic Manifolds
We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell’s transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical stru...
متن کاملFirst Steps in Symplectic and Spectral Theory of Integrable Systems
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best approach to such a large classification task would be, it is possible to single out some promising directions and preliminary problems. This paper discusses them an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2004
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2003.09.011