The Elliptic and Hyperbolic fixed points in the Henon- Heiles Potential

Abstract

In this report the trajectories in the Henon-Heiles potential V_(x/y) = ¹/₂ (x² + y²) + x²y - ^y2/₃ were integrated using the fourth order Runge-Kutta algorithm at some fixed energy levels while the initial conditions of the position [y] and the momentum conjugate [P_y] were varied, the corresponding Poincare maps (surface of sections) were plotted which satisfies the condition for a dynamical system to be chaotic.

Keywords: Hyberbolic, Momentum, Topology, Elliptic,