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.
