Modelling chaotic Hamiltonian systems as a Markov Chain
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their trajectories intersect Poincaré section q1 = 0, p1>0 , these intersections are random. To determine how random they are we shall model the intersections as a Markov chain and show that these intersections describe a closed ergodic Markov chain with a doubly stochastic matrix ∑π=∑π=1. This is true for these systems with an error of +-2%.
Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 199-202