RIGOROUS COMPUTATIONAL SHADOWING OF ORBITS OF ORDINARY DIFFERENTIAL-EQUATIONS

The existence of a true orbit near a numerically computed approximate orbit - shadowing - of autonomous system of ordinary differential equa tions is investigated. A general shadowing theorem for finite time, wh ich guarantees the existence of shadowing in ordinary differential equ ations and provides error bounds for the distance between the true and the approximate orbit in terms of computable quantities, is proved. T he practical use and the effectiveness of this theorem is demonstrated in the numerical computations of chaotic orbits of the Lorenz equatio ns.