Symbolic research of the periodic solutions of the nonintegrable Hamiltonian system of Ollongren

摘要: The main aim of this work is to look for the periodic solutions nonintegrable Hamiltonian system Ollongren in neighborhood origin. We apply a functional algorithm derived from method Lindstedt-Poincare. first show that admits six families and then, by means computer algebra “Mathematica”, compute series corresponding these up O(e14A29) as well their periods O(e15A30), where A zeroth-order amplitude έ perturbative parameter. Reducing one degree freedom we also prove period two “oblique” rigorously equal Gauss hypergeometric series. Moreover, study numerically convergence L-P test validity using numerical integration technique. Finally, compare our results with those geometrical Lie method.