Spatially localized unstable periodic orbits of a high-dimensional chaotic system

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 attractor’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. © 1998 The American Physical Society.

Duke Scholars

Author Henry Greenside Physics