Periodic orbits of the three dimensional logarithm galactic potential (Q668631)

The authors consider the Hamiltonian \[H(x,y,z,p_x,p_y,p_z)=\frac12(p_x^2+p_y^2+p_z^2)+V(x,y,z),\] where the potential $V$ is given by \[V(x,y,z)=\frac{v_0^2}{2}\ln (x^2-\lambda x^3+a y^2 + bz^2+c_b^2).\] After performing a scaling of the coordinates and momenta, the first order averaging method is used in order to study the existence of periodic orbits of the corresponding Hamiltonian system.