Regular and chaotic motions in Hénon-Heiles like Hamiltonian

Authors: IDUGBA MATHIAS ECHI, ALEXANDER NWABEZE AMAH, EMMANUEL ANTHONY

Abstract: The dynamics of a system subjected to a potential equal to the sum of the Hénon--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 Poincaré 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 Poincaré 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.

Keywords: Hamiltonian, Hénon-Heiles, Poincaré section, Lyapunov exponent, autocorrelation

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