Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory

Abstract

Abstract. We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. The Hamiltonian system here studied comes either from the analyze of the galactic dynamics, or from the motion of the atomic particles in physics.

Complex Dynamics of Some Hamiltonian Systems: Nonintegrability of Equations of Motion

“…We denote by 1 , 2 , and the differential Galois group of the equations (38), (39), and (37), respectively, over the field of rational functions on Γ. As a representation of an element of is of the form…”

“…where 0 is the 2 × 2 null matrix, ∈ 1 , and ∈ 2 , the identity component of is not Abelian if the identity component of 1 or 2 is not Abelian. Then, we turn to consider the normal variational equation (38) and analyze the differential Galois group 1 .…”