Quasi-polynomial Systems

Abstract

Numerical or analytical investigation of systems of differential equations is usually greatly facilitated if the right-hand sides of the equations are polynomials with respect to the unknown functions (polynomial systems). Such systems occur quite naturally in celestial mechanics in dealing with solutions in the vicinity of some known particular solution, in investigating the long- term evolution of the planetary orbits for small eccentricities and inclinations (the secular system) and so on. Moreover, the differential equations of celestial mechanics may be reduced in typical cases to polynomial systems by introducing some extra unknown variables. To illustrate this let us consider the problem of the heliocentric motion of N planets.