  In this paper we study the infinitesimal symmetries, Newtonoid vector fields,
infinitesimal Noether symmetries and conservation laws of Hamiltonian systems.
Using the dynamical covariant derivative and Jacobi endomorphism on the
cotangent bundle we find the invariant equations of infinitesimal symmetries
and Newtonoid vector fields and prove that the canonical nonlinear connection
induced by a regular Hamiltonian can be determined by these symmetries.
Finally, an example from optimal control theory is given.
