Symmetries and conservation laws of Hamiltonian systems

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.