Topological entropy

Summary

Topological entropy is a nonnegative number, possibly infinite, that measures the exponential growth rate of the number of distinguishable orbits of a continuous map. It is an invariant of topological conjugacy, so it can show that two systems are not conjugate. Positive entropy is a common sign of complicated, chaotic behaviour. Through the variational principle it equals the supremum of the measure-theoretic entropies of the invariant measures.