It is known that the Julia set of the mapping z→λexp(z) with λ】 e<sup>-1</sup> is the whole plane (R. L. Devaney). In this paper, it is proved that for any given λ】e<sup>-1</sup> ther...It is known that the Julia set of the mapping z→λexp(z) with λ】 e<sup>-1</sup> is the whole plane (R. L. Devaney). In this paper, it is proved that for any given λ】e<sup>-1</sup> there is a sequence of complex number λ<sub>j</sub><sup>*</sup>∈C such that λ<sub>j</sub><sup>*</sup>→(as j→∞) and the Julia setof z→λ<sub>j</sub><sup>*</sup>exp(z) is not the whole plane. Hence λexp(z) (λ】e<sup>-1</sup>) is not structurally stable.展开更多
文摘It is known that the Julia set of the mapping z→λexp(z) with λ】 e<sup>-1</sup> is the whole plane (R. L. Devaney). In this paper, it is proved that for any given λ】e<sup>-1</sup> there is a sequence of complex number λ<sub>j</sub><sup>*</sup>∈C such that λ<sub>j</sub><sup>*</sup>→(as j→∞) and the Julia setof z→λ<sub>j</sub><sup>*</sup>exp(z) is not the whole plane. Hence λexp(z) (λ】e<sup>-1</sup>) is not structurally stable.