Spatially Localized Unstable Periodic Orbits

Details Spatially Localized Unstable Periodic Orbits Spatially Localized Unstable Periodic Orbits

1997-04-03

arxiv.org/abs/chao-dyn/9704005v3

Nonlinear Sciences

Chaotic Dynamics

16 pages (total), 3 eps figures (Includes two new references and a new footnote) Submitted to Physical Review Letters

Scientific paper

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.

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