INSTABILITY OF N-BODY SYSTEMS - CAN COMPUTERS SOLVE THE PROBLEM

The problem of the numerical study of instability of N-body gravitatin g systems by means of Lyapunov characteristic exponents is considered. The discontinuity of Lyapunov exponents is shown for computer-created systems both with softened and, what is more interesting, unsoftened (i.e. pure Newtonian) potentials. The Lyapunov technique thus cannot b e considered as an appropriate method of study of N-body systems, and physical and astrophysical interpretations of results of previous comp uter studies appear to be unfounded.