94-54 M. Blank

Pathologies generated by round-off in dynamical systems (70K, TeX) Mar 4, 94

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Abstract. When solving differential equations or other dynamical systems on a computer, the effect of finiteness (round-off) can sometimes be very drastic. We discuss on the one hand rigorous conditions under which statistical (the most rough) properties of the system survive discretization, and on another hand examples where, even in the limit of vanishing perturbation, a "localization" phenomenon takes place: trajectories which should normally be dense remain confined to a small number of points. In some instances, the addition of a small amount of true noise can cure the pathologies. From the point of view of computer theory questions that we shall consider may seem very simple, but often they lead to quite nontrivial mathematical constructions.

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