A geometrical method towards first integrals for dynamical systems
arXiv:solv-int/9608007 · doi:10.1063/1.531772
Abstract
We develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements' form. We apply it to three dynamical systems: Lotka--Volterra, Lorenz and Rikitake.
15 pages, RevTeX with aps and prb styles