Symplectic and Hamiltonian Group Actions

In this chapter, we define symplectic and Hamiltonian actions. These are the main topics of this book, so that we spend some time on their properties. Hamiltonian actions of tori of maximal dimension are a special case of integrable systems. We prove (this is the Arnold―Liouville theorem), that they are also the local form of all integrable systems with compact level sets. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.