Spatially Localized Unstable Periodic Orbits

1997/04/03 by Scott M. Zoldi, Zoldi, Scott M., Henry Greenside +2
Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Control and Dynamics of Mobile Robots #FOS: Physical sciences #chao-dyn #nlin.CD

paper · pdf · doi:10.48550/arxiv.chao-dyn/9704005

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

openalex publication_date 1997/04/03 · arxiv created 1997/04/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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