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 stat e spaces a simple model explains some of the geometrical features of the le vel contours, which is illustrated by numerical data for a driven damped pe ndulum, where unstable periodic orbits modulate predictability, and for the Lorenz system, where the stable manifold of a fixed point provides the dom inant features. The spiral structure of the latter is given in terms of Bes sel functions. (C) 1999 Elsevier Science Ltd. All rights reserved.