Partition-Based Entropies of Deterministic and Stochastic Maps

In this paper we explore the relationship between the Kolmogorov–Sinai entropy, the sum of positive Lyapunov exponents, denoted here as the Pesin entropy and a new measure, the T-entropy, for nonlinear maps. We demonstrate that threshold-crossing partitions are effective in deriving representative symbolic realisations for the real-valued time series. We describe the recently developed entropy measure for finite strings and compare with values derived from the application of Shannon's theory. These techniques are further applied to a simple stochastic system, appearing to further confirm recent theoretical results on Lyapunov exponents.