Summary: Instituto Superior T´ecnico
Departamento de Matem´atica
SYMPLECTIC GEOMETRY - 2nd
Problem Set 2
Due date: March 31
1. Let (M, ) be a symplectic manifold, : M M a symplectomorphism and h : M
R a smooth function. Show that the Hamiltonian vector fields Xh and Xh-1 satisfy
Xh-1 = Xh .
2. Let L be a smooth manifold and T
L its cotangent bundle equipped with the canonical
symplectic form can = -dcan. Let also h : L R be a smooth function and
h : T
L a diffeomorphism defined by
h(x, ) = (x, + dhx) , x L , T
x L .