Detecting order and chaos in three-dimensional Hamiltonian systems by geometrical methods

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 2):046220. doi: 10.1103/PhysRevE.76.046220. Epub 2007 Oct 23.

Abstract

We use a geometrical method to distinguish between ordered and chaotic motion in three-dimensional Hamiltonian systems. We show that this method gives results in agreement with the computation of Lyapunov characteristic exponents. We discuss some examples of unstable Hamiltonian systems in three dimensions, giving, as a particular illustration, detailed results for a potential obtained from a Hamiltonian obtained from a Yang-Mills system.