CONTENTSIntroductionChapter I. Differentiation in Cartesian products of normed and infrabarrelled of DF-type spaces§ 1. Preliminaries......................................................................................................................................................................... 7§ 2. Fundamental definitions...................................................................................................................................................... 7§ 3. Certain properties...
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.
The notions of the dual double vector bundle and the dual double vector bundle morphism are defined. Theorems on canonical isomorphisms are formulated and proved. Several examples are given.
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