Julia set

Julia set is set of values, that fall out from the range of holomorphism of some given function. Julia set is often defined with symbol $J$ or $\mathbb J$. The name of the function can be indicated as subscript or in parenthesis immediately after this symbol.

Let $f$ be holomorphic function defined at some $C\in \mathbb C$.

Then

$\mathbb J(f) = \{ z \in C : \exists ~ n\in \mathbb N_+ ~,~ f^n(z) \bar \in C\}$