Difference between revisions of "Julia set"
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| − | [[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. |
+ | [[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 either as the subscript or in parenthesis immediately after this symbol. |
Let $f$ be holomorphic function defined at some $C\in \mathbb C$. |
Let $f$ be holomorphic function defined at some $C\in \mathbb C$. |
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Revision as of 12:34, 10 July 2013
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 either as the subscript or in parenthesis immediately after this symbol.
Let $f$ be holomorphic function defined at some $C\in \mathbb C$.
Then
$\mathbb J(f) = \{ z \in C : \exists ~ n\in \mathbb N_+ ~,~ f^n(z) \bar \in C\}$