  In this paper we present canonical and canonoid transformations considered as
global geometrical objects for Hamiltonian systems. Under the mathematical
formalisms of symplectic, cosymplectic, contact and cocontact geometry, the
canonoid transformations are defined for (co)symplectic, (co)contact
Hamiltonian systems, respectively. The local characterizations of these
transformations is derived explicitly and it is demonstrated that for a given
canonoid transformation there exist constants of motion associated with it
