Topological Entropy

In mathematics, the topological entropy of a topological dynamical system is a nonnegative extended real number that measures the complexity of the system behavior over time. It was introduced in 1965 by Adler, Konheim and McAndrew, drawing on the earlier idea of Kolmogorov-Sinai entropy, and was later given an alternative, more transparent formulation by Efim Dinaburg and Rufus Bowen: for systems generated by iterating a function, topological entropy measures the exponential growth rate, as time increases, in the number of orbits that can still be told apart. A result called the variational principle connects topological entropy to the measure-theoretic notions of entropy defined for the same dynamical system.