%0 Journal Article %1 Lan_2004 %A Lan, Yueheng %A Cvitanović, Predrag %D 2004 %I American Physical Society %J Phys. Rev. E %K chaotic-attractors kuramoto-sivashinksy periodic-orbit-theory %N 1 %P 016217 %R 10.1103/PhysRevE.69.016217 %T Variational method for finding periodic orbits in a general flow %U http://link.aps.org/doi/10.1103/PhysRevE.69.016217 %V 69 %X 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 Henon-Heiles system, the circular restricted three-body problem, and the Kuramoto-Sivashinsky system in a weakly turbulent regime.

@article{Lan_2004, abstract = {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 Henon-Heiles system, the circular restricted three-body problem, and the Kuramoto-Sivashinsky system in a weakly turbulent regime.}, added-at = {2013-02-15T16:46:40.000+0100}, author = {Lan, Yueheng and Cvitanović, Predrag}, biburl = {https://www.bibsonomy.org/bibtex/24652d7ed5dc85901b501a699039b4435/knielson}, description = {Phys. Rev. E 69, 016217 (2004): Variational method for finding periodic orbits in a general flow}, doi = {10.1103/PhysRevE.69.016217}, interhash = {d93177563f7a69d56f3156e9f0b3fce0}, intrahash = {4652d7ed5dc85901b501a699039b4435}, journal = {Phys. Rev. E}, keywords = {chaotic-attractors kuramoto-sivashinksy periodic-orbit-theory}, month = jan, number = 1, numpages = {10}, pages = 016217, publisher = {American Physical Society}, timestamp = {2013-02-15T16:46:40.000+0100}, title = {Variational method for finding periodic orbits in a general flow}, url = {http://link.aps.org/doi/10.1103/PhysRevE.69.016217}, volume = 69, year = 2004 }