Hamiltonian Systems on Linear Symplectic Spaces

Abstract

A natural arena for Hamiltonian mechanics is a symplectic or Poisson manifold. The next few chapters concentrate on the symplectic case, while Chapter 10 introduces the Poisson case. The symplectic context focuses on the symplectic two-form $\sum {d{q^i} \wedge d{p_i}}$ and its infinite-dimensional analogues, while the Poisson context looks at the Poisson bracket as the fundamental object.