  This report investigates the dynamical stability conjectures of Palis and
Smale, and Pugh and Shub from the standpoint of numerical observation and lays
the foundation for a stability conjecture. As the dimension of a dissipative
dynamical system is increased, it is observed that the number of positive
Lyapunov exponents increases monotonically, the Lyapunov exponents tend towards
continuous change with respect to parameter variation, the number of observable
periodic windows decreases (at least below numerical precision), and a subset
of parameter space exists such that topological change is very common with
small parameter perturbation. However, this seemingly inevitable topological
variation is never catastrophic (the dynamic type is preserved) if the
dimension of the system is high enough.
