Regular and chaotic motions in Henon-Heiles like Hamiltonian

The dynamics of a system subjected to a potential equal to the sum of the Henon-Heiles potential and that of hydrogen in an electric field was studied. The 4 Hamilton s equations of motion follow from the Hamiltonian and they were integrated numerically using the Runge-Kutta fourth order method. The Poincare surface of a section fixed at x = 0 and px 0 was used to reduce the phase space to a 2-dimensional plane. The analysis of the Poincare surface, the Lyapunov exponent, and the autocorrelation shows that as the constant of motion, E, increases from 0.30 to 0.45, the dynamics makes a transition from periodic and quasi-periodic to chaotic motions.