Zoldi, SM; Greenside, HS, *Spatially localized unstable periodic orbits of a high-dimensional chaotic system*,
Physical Review E Statistical, Nonlinear, and Soft Matter Physics, vol. 57 no. 3
(January, 1998),
pp. R2511-R2514, American Physical Society (APS) [doi] .
**Abstract:**

*Using an innovative damped-Newton method, we report the calculation and analysis of many distinct unstable periodic orbits (UPOs) for a high-fractal-dimension [formula presented] extensively chaotic solution of a 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 escape-time weighting of 127 UPOs, the attractorâ€™s fractal dimension can be estimated with a relative error of 2%. Statistical errors are found to decrease as [formula presented] as the number [formula presented] of known UPOs increases. Â© 1998 The American Physical Society.*