Hamiltonian structures for projectable dynamics on symplectic fiber bundles
This work is a study of the Hamiltonization problem for projectable dynamics on general symplectic bundles. Let us recall that linearized dynamics does not inherit any natural Hamiltonian structure in general. The Hamiltonization problem for linearized dynamics has been extensively developed. In this paper, the purpose is to study this problem in a general setting. The author obtains necessary and sufficient conditions for the existence of Hamiltonian structures in terms of invariant symplectic connections. When the symplectic bundle is flat, it is proved that the conditions lead to study the solvability of linear differential equations of the homological type. Some versions of the conditions in the cases of exact symplectic bundles and symplectic vector bundles are also discussed.
scientific article; zbMATH DE number 6155708