ON THE COMPUTATION OF ALL THE EQUILIBRIUM POINTS IN HAMILTONIAN SYSTEMS WITH THREE DEGREES OF FREEDOM

In dynamical system theory the determination of the equilibrium points often requires the solution of systems of transcendental equations, whose exact number of solutions cannot be found analytically. In this paper, topological degree theory (especially the Kronecker-Picard integral) is implemented to obtain the exact number of these solutions, within a given region. These results are studied and applied to the accurate computation of the total number of equilibrium points of Hamiltonian systems with three degrees of freedom.