A Hamiltonian diffeomorphism is the time-one map of a Hamiltonian isotopy on a symplectic manifold. It is
a symplectic diffeomorphism, but preservation
of the symplectic form alone does not imply that
a diffeomorphism is Hamiltonian. A fixed
point 
is nondegenerate when 
is invertible. For a specified generating isotopy,
a fixed point determines the periodic orbit 
. Its contractibility refers to this
loop in the manifold, so the
generating path is part of that condition.
The Arnold conjecture relates fixed point counts to critical point counts of smooth functions.
