In this chapter, we consider systems with irregular dynamical behaviors that are stronger than ergodic. Namely, we consider dynamics described by measure preserving transformations that have the property of strong, or Hopf, mixing. Systems with mixing dynamics have entropies that are forever fixed by their mode of preparation. This is followed by a brief discussion of Kolmogorov systems in Section B. Section C discusses the behavior of temporal correlation between dynamical variables, showing that mixing is necessary and sufficient for the decay of temporal correlations to zero.
Unable to display preview. Download preview PDF.