Julia set of λ exp(z)/z with real parameters λ
Julia set of λ exp(z)/z with real parameters λ
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DOI：
10.1007/s13226-017-0225-8
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发表时间：
2017-06
影响因子：
0.7
通讯作者：
Guoping Zhan
中科院分区：
文献类型：
--
作者：
Guoping Zhan
本文研究了具有真实的参数λ的函数族λ exp（z）/z的Julia集.我们寻找什么样的真实的参数λ的值使得λ exp（z）/z的Julia集不与整个平面重合，从而给出了真实的参数的完全分类，这类似于Jang关于一族超越整函数的结果.此外，还讨论了当Julia集不是全平面时，λ exp（z）/z中带真实的参数λ的Fatou集和Julia集的形状和大小.
In this paper, we investigate the Julia set of the family λ exp(z)/zwith real parameters λ. We look for what values of real parameters λ such that the Julia set of λ exp(z)/zdoes not coincide with the whole plane, and thus gives a complete classification for real parameters, which is similar to Jang’s result of a family of transcendental entire functions. Moreover, We also discuss the shape and size of Fatou sets and Julia sets of λ exp(z)/zwith real parameters λ when the Julia sets are not the whole plane.