Yueheng Lan, Predrag Cvitanovic
Variational method for finding periodic orbits in a general flow
(221K, APS-REVTEX)
ABSTRACT. A variational principle for determining unstable periodic orbits of
flows as well as unstable spatio-temporally periodic solutions of
extended systems is proposed and implemented. 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 Henon-Heiles system,
the circular restricted three-body problem,
and the Kuramoto-Sivashinsky system in a weakly turbulent regime.