Topological Entropy

A nonnegative extended real number that quantifies the exponential growth rate of the number of distinguishable orbit segments of a continuous self-map on a compact topological (or metric) space; it can be defined via open covers, separated/spanning sets, or (for shifts) growth of admissible words.

A nonnegative real number (possibly infinite) assigned to a continuous self-map that measures the exponential growth rate of distinguishable orbit segments under iteration and is invariant under topological conjugacy.