%0 Journal Article %1 Lan_2008 %A Lan, Yueheng %A Cvitanović, Predrag %D 2008 %I American Physical Society %J Phys. Rev. E %K kuramoto-sivashinksy %N 2 %P 026208 %R 10.1103/PhysRevE.78.026208 %T Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics %U http://link.aps.org/doi/10.1103/PhysRevE.78.026208 %V 78 %X We undertake an exploration of recurrent patterns in the antisymmetric subspace of the one-dimensional Kuramoto-Sivashinsky system. For a small but already rather "turbulent" system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. The Newton descent method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin-its backbone consists of several Smale horseshoe repellers, well approximated by intrinsic local one-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.

@article{Lan_2008, abstract = {We undertake an exploration of recurrent patterns in the antisymmetric subspace of the one-dimensional Kuramoto-Sivashinsky system. For a small but already rather "turbulent" system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. The Newton descent method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin-its backbone consists of several Smale horseshoe repellers, well approximated by intrinsic local one-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.}, added-at = {2013-02-15T16:22:56.000+0100}, author = {Lan, Yueheng and Cvitanović, Predrag}, biburl = {https://www.bibsonomy.org/bibtex/290d2491b8b7d92edb4c7555af439f42d/knielson}, description = {Phys. Rev. E 78, 026208 (2008): Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics}, doi = {10.1103/PhysRevE.78.026208}, interhash = {d1d4ac820c49341647b1b7d1be415173}, intrahash = {90d2491b8b7d92edb4c7555af439f42d}, journal = {Phys. Rev. E}, keywords = {kuramoto-sivashinksy}, month = aug, number = 2, numpages = {12}, pages = 026208, publisher = {American Physical Society}, timestamp = {2013-02-15T16:22:56.000+0100}, title = {Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics}, url = {http://link.aps.org/doi/10.1103/PhysRevE.78.026208}, volume = 78, year = 2008 }