Zoldi, SM; Greenside, HS, *Spatially localized unstable periodic orbits of a high-dimensional chaotic system*,
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 57 no. 3 SUPPL. A
(1998),
pp. R2511-R2514 .
**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 (D = 8.8) 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 attractor's fractal dimension can be estimated with a relative error of 2%. Statistical errors are found to decrease as l/√N as the number N of known UPOs increases.*