Symmetries of some classes of dynamical systems

In this paper a three-dimensional system with five parameters is considered. For some particular values of these parameters, one finds known dynamical systems. The purpose of this work is to study some symmetries of the considered system, such as Lie-point symmetries, conformal symmetries, master symmetries and variational symmetries. In order to present these symmetries we give constants of motion. Using Lie group theory, Hamiltonian and bi-Hamiltonian structures are given. Also, symplectic realizations of Hamiltonian structures are presented. We have generalized some known results and we have established other new results. Our unitary presentation allows the study of these classes of dynamical systems from other points of view, e.g. stability problems, existence of periodic orbits, homoclinic and heteroclinic orbits.