Spatially Localized Unstable Periodic Orbits
chao-dyn
2008-02-03 v3 Chaotic Dynamics
Abstract
Using an innovative damped-Newton method, we report the first calculation of many distinct unstable periodic orbits (UPOs) of a large high-dimensional extensively chaotic partial differential equation. A majority of the UPOs turn out to be spatially localized in that time dependence occurs only on portions of the spatial domain. With a particular weighting of 127 UPOs, the Lyapunov fractal dimension D=8.8 can be estimated with a relative error of 2%. We discuss the implications of these spatially localized UPOs for understanding and controlling spatiotemporal chaos.
Keywords
Cite
@article{arxiv.chao-dyn/9704005,
title = {Spatially Localized Unstable Periodic Orbits},
author = {Scott M. Zoldi and Henry S. Greenside},
journal= {arXiv preprint arXiv:chao-dyn/9704005},
year = {2008}
}
Comments
16 pages (total), 3 eps figures (Includes two new references and a new footnote) Submitted to Physical Review Letters