The stability of saturated linear dynamical systems is undecidable

We prove that several global properties (global convergence, global asympto tic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only f or point-to-point properties. We prove these properties undecidable for sat urated linear dynamical systems, and for continuous piecewise affine dynami cal systems in dimension 3. We also describe some consequences of our resul ts on the possible dynamics of such systems. (C) 2001 Academic Press.