Hamiltonian formalism for fiberwise linear dynamical systems (Q5931993)

The goal of this paper is to present a Hamiltonian formalism for a special class of autonomous dynamical systems on vector bundles, namely, the fiberwise linear system. Two types of results are presented: a) a Hamiltonization criterion is formulated as the solvability of some differential equations on the base including a matrix equation of Lax's type; b) geometric interpretation of these equations is given in terms of symplectic connections. As an application of the main results, the authors discuss an interpretation of the Hamiltonization problem in the context of normal forms.