UNSTABLE EVOLUTION OF POINTWISE TRAJECTORY SOLUTIONS TO CHAOTIC MAPS

Simple chaotic maps are used to illustrate the inherent instability of trajectory solutions to the Frobenius-Perron equation. This is demons trated by the difference in the behavior of delta-function solutions a nd of extended densities. Extended densities evolve asymptotically and irreversibly into invariant measures on stationary attractors. Pointw ise trajectories chaotically roam over these attractors forever. Perio dic Gaussian distributions on the unit interval are used to provide in sight. Viewing evolving densities as ensembles of unstable pointwise t rajectories gives densities a stochastic interpretation. (C) 1995 Amer ican Institute of Physics.