The denotations of Julia sets of transcendental entire functions
Let \(f\) be an entire transcendental function, \(F(f)\) its Fatou set and \(J(f)\) its Julia set. Then \(J(f)\subset\overline{\bigcup^{\infty}_{n=0}f^{-n}(a)}\) if \(a\in{\mathbb C}\) is not a Fatou exceptional value. If \(a\in J(f)\), then we have equality. The authors claim that we have equality also for certain \(a\in F(f)\). As \(\bigcup^{\infty}_{n=0}f^{-n}(a)\subset F(f)\) for \(a\in F(f)\) by the complete invariance of \(F(f)\), this statement seems to be false.
scientific article; zbMATH DE number 1616451