Persistent Chaos in High Dimensions

As the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this seemingly inevitable (and expected) topological change is never catastrophic, in the sense that the behavior type is preserved. One concludes that deterministic chaos is persistent in high dimensions.