Abstract
In this paper we show that the Julia set g ( λ sin z) is the whole plane C for certain real λ with ¦λ¦ > 1 by considering some connections between the chaotic set of λ sin x with xϵ[−λ,λ]⊂ R and the Julia set of λ sin with zϵ C . Denote by F a 1, a 2, a 3, a 4 the function a 1 sin( a 2 z + a 3) + a 4. We also show that J (FF a 1,a 2,a 3,a 4 = C for certain complex parameters a 1, a 2, a 3, and a 4 by considering the dynamical behaviour of the singularities of F a 1, a 2, a 3, a 4 −1 under F a 1, a 2, a 3, a 4 . The idea used in the proof of Theorem 1 can also be applicable to more general functions.
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