Georgia Institute of Technology College of Sciences

Permutation entropy was introduced as a complexity measure of time series. Formally, it replaces the symbol blocks in the definition of Shannon entropy by the so-called ordinal patterns –a digest of the ups-and-downs along a finite orbit in a totally ordered state space. Later, this concept was extended to self maps of n-dimensional intervals, in metric and topological versions. It can be proven that, under some assumptions, the metric and topological permutation entropy coincide with their corresponding conventional counterparts. Besides its use as an entropy estimator, permutation entropy has found some interesting applications. We will talk about the detection of determinism in noisy time series, and the recovery of the control parameter from the symbolic sequences of a unimodal map (which allows to cryptanalize some chaotic ciphers).