Chaos in Dynamical Systems: How Uncertainty Arises in Scientific and Engineering Phenomena

The two preceding chapters analyzed the phenomenon of randomness from the viewpoint of algorithmic and computational complexity of a fixed string of data, and in the context of the formal mathematical probability theory based on Kolmogorov’s concept of a sequence of statistically independent random variables. We complete this picture in the present chapter by demonstrating that certain, seemingly deterministic, dynamical systems also exhibit some attributes of randomness such as stability of frequencies and fluctuations. The essential features here are nonlinearity and/or sensitive dependence on initial conditions.