Variational method for finding periodic orbits in a general flow

Details Variational method for finding periodic orbits in a general flow Variational method for finding periodic orbits in a general flow

2003-08-05

arxiv.org/abs/nlin/0308008v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 5 figures

Scientific paper

10.1103/PhysRevE.69.016217

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 ``\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 H\'enon-Heiles system, the circular restricted three-body problem, and the Kuramoto-Sivashinsky system in a weakly turbulent regime.

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