Julia set

(redirected from Fatou set)
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Related to Fatou set: Julia Sets

Ju·li·a set

 (jo͞o′lē-ə)
n.
For any holomorphic function on a complex plane, the boundary of the set of points whose result diverges when the function is iteratively evaluated at each point.

[After Gaston Julia (1893-1978), French mathematician.]
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References in periodicals archive ?
For a rational map f: [P.sup.1.sub.K] [right arrow] [P.sup.1.sub.K], the Fatou set is defined as the largest open set of [P.sup.1.sub.K] on which [{[f.sup.k]}.sup.[infinity].sub.
The complementary of J(R) in the Riemann sphere is the Fatou set F(R).
The dynamics of this rational map induces a subdivision of the complex sphere into two sets, namely, the Fatou set F(R) and the Julia set J(R) of R.
Definition: The set of all orbits that either converge to a value or diverge (which can also be considered converging to infinity) is called the Fatou set. The complement of the Fatou set is the Julia set.