Notes on symplectic geometry

Athanassopoulos K.

Contents1. Introduction 1.1 Newtonian mechaics 1.2 Lagrangian mechanics 1.3 The equationsof Hamilton 2. Sympletic spaces 2.1 Sympletic vector spaces 2.2 Sympletic manifolds 2.3 Local description of sympletic manifolds 2.4 Hamiltonian vector fields and Poisson bracket 2.5 Coadjoint orbits 2.6 homogeneous sympletic manifolds 2.7 Poisson manifolds3. Symmetries and integrability 3.1 Sympletic group actions 3.2 Momentum maps 3.3 Sympletic reduction 3.4 Completely integrable Hamiltonian systems