2.2 Symplectic structure on
2.3 Symplectic mappings
2.4 Hamiltonian vector fields
2.5 Lagrangian submanifolds
We provide in this chapter a quick discussion of the symplectic geometric
and its interplay with Hamiltonian dynamics.
These will be important for our later goal of understanding interrelationships
between dynamics and PDE.
The reader may wish to first review our basic notation and also the
theory of differential forms, set forth, respectively, in Appendices A and B.
Let V :
denote a smooth vector field. Fix a point z ∈
solve the ordinary differential equations (ODE)
˙ w = V (w) (t ∈ R)
w(0) = z,