M. Blank
Pathologies generated by round-off in dynamical systems
(70K, TeX)
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.