Introduction to differentiable manifolds and symplectic geometry
As the title of this paper says, the author presents an elementary introduction to symplectic geometry. He starts with a motivation of the Hamiltonian approach to mechanics. In order to introduce the symplectic geometry, he develops in the chapters 1 and 2 multilinear algebra and symplectic algebra, as well as the theory of finite dimensional manifolds. More precisely, the notions of differentiable manifold, Lie group, vector bundle, tangent bundle and the calculus of differential forms on manifolds are exhibited. The last chapter is dedicated to the study of the symplectic geometry and Hamiltonian dynamical systems.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00053].
scientific article; zbMATH DE number 1664354