Stable manifolds and predictability of dynamical systems

The predictability of dissipative dynamical systems varies with their state. The level contours of predictability closely follow the stable manifolds of the most unstable sets of nonwandering points. In three-dimensional state spaces a simple model explains some of the geometrical features of the level contours, which is illustrated by numerical data for a driven damped pendulum, where unstable periodic orbits modulate predictability, and for the Lorenz system, where the stable manifold of a fixed point provides the dominant features. The spiral structure of the latter is given in terms of Bessel functions. (C) 1999 Elsevier Science Ltd. All rights reserved.