Integrability of one particle in a perturbed central quartic potential

Abstract

We show here that the Hamiltonian (1.1) has n functionally independent integrals of motion in involution which are rational both in phase space variables and in parameters. Moreover these integrals are quadratic in momenta and the Hamilton-Jacobi equation of the system (1.1) is separable in generalized elliptic coordinates. A Lax representation for (1.1) and for higher flows is found. The system (1.1) constrained to an ellipsoid remains integrable. © 1985 IOP Publishing Ltd.