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In mathematics, and particularly complex dynamics, the escaping set of an entire function ƒ consists of all points that tend to infinity under the repeated application of ƒ.That is, a complex number z 0 ∈ C {\displaystyle z_{0}\in \mathbb {C} } belongs to the escaping set if and only if the sequence defined by z n + 1 := f {\displaystyle z_{n+1}:=f} converges to infinity as n {\displaystyle n} gets large. The escaping set of f {\displaystyle f} is denoted by I {\displaystyle I}.
For example, for f = e z {\displaystyle f=e^{z}} , the origin belongs to the escaping set, since the sequence
tends to infinity.