On the analytic integrability of the cored galactic Hamiltonian

Abstract

Abstract. We provide a complete characterization of the analytic first integrals of the cored galactic Hamiltonian.

Periodic orbits of the generalized Friedmann-Robertson-Walker potential in galactic dynamics in a rotating reference frame

“…1 In the last years, the most of work on galactic dynamic has been restricted to the models of elliptical galaxies (for more details see, e.g., Ref. [2][3][4][5][6][7][8]. The majority of galactic potential has symmetry about the two axes and thus, it can be written in the form V (x 2 , y 2 ).…”

“…This study gives the sufficient conditions on the two parameters, b and ω, in order to guarantee the existence of continuous families of periodic solutions that are parameterized by the energy constant h. These results are collected and summarized in the following theorem: Theorem 1. For sufficiently small ε 0 and on the non-zero level of Jacobi integral (6), the Hamilton equations (4) It is well known that the Hamilton equations (4) is completely integrable if one additional integral of motion that is independent on the Jacobi integral (6) exists. We prove that the Hamilton equations (4) cannot admit any additional integral besides the Jacobi integral using one of the obtained periodic solutions.…”