Variational method for finding periodic orbits in a general flow.
A variational principle is proposed and implemented for determining unstable periodic orbits of flows as well as unstable spatiotemporally periodic solutions of extended systems. An initial loop approximating a periodic solution is evolved in the space of loops toward a true periodic solution by a minimization of local errors along the loop. The "Newton descent" partial differential equation that governs this evolution is an infinitesimal step version of the damped Newton-Raphson iteration. The feasibility of the method is demonstrated by its application to the Hénon-Heiles system, the circular restricted three-body problem, and the Kuramoto-Sivashinsky system in a weakly turbulent regime.
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA. gte158y@prism.gatech.edu
Yueheng
Y
Lan
Predrag
P
Cvitanović