Expansivity constant

In mathematics, the notion of expansivity formalizes the notion of points moving away from one another under the action of an iterated function. The idea of expansivity is fairly rigid, as the definition of positive expansivity, below, as well as the Schwarz–Ahlfors–Pick theorem demonstrate.

If ${\displaystyle (X,d)}$ is a metric space, a homeomorphism ${\displaystyle f\colon X\to X}$ is said to be expansive if there is a constant

called the expansivity constant, such that for every pair of points ${\displaystyle x\neq y}$ in ${\displaystyle X}$ there is an integer ${\displaystyle n}$ such that

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