Equilibrium points and periodic orbits of higher order autonomous generalized Birkhoff system

Abstract

Equilibrium points and periodic orbits of a higher order autonomous generalized Birkhoff system are studied by using qualitative methods of ordinary differential equations and the Liapunov center theorem. First, the equilibrium points and their properties are obtained from the equations of equilibrium points. Then, the characteristic roots of the Frechet derivative C are obtained, and the type of equilibrium points of the system is verified. Finally, the existence theorem of periodic orbits is given by the Liapunov center theorem.