CHAMPS

Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors.

A.S. Demian and S. Wiggins, Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors, International Journal of Bifurcation and Chaos, 27 (4), 1750225 (2017).

http://www.worldscientific.com/doi/abs/10.1142/S021812741750225X

 The purpose of this paper is to apply Lagrangian Descriptors, a concept used to describe phase space structure, to autonomous Hamiltonian systems with two degrees of freedom in order to detect periodic solutions. We propose a method for Hamiltonian systems with saddle-center equilibrium and apply this approach to the classical Hénon–Heiles system. The method was successful in locating the unstable Lyapunov orbits in phase space.