Singular perturbations in the quadratic family
Singular perturbations in the quadratic family
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DOI：
10.1080/10236190701702429
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发表时间：
2008-05
影响因子：
1.1
通讯作者：
Sebastian M. Marotta
中科院分区：
文献类型：
--
作者：
Sebastian M. Marotta
本文研究了由给出的复映射族的动力学，其中c和λ是复参数，使得c位于Mandelbrot集的双曲分支的内部，但不在其中心，且λ是任意小的.我们证明了F λ的Julia集由与F0的Julia集同胚的曲线的倒拷贝的可数集合和在这些曲线的每一个上积累的不可数的点分量组成。
In this paper, we study the dynamics of the family of complex maps given by , where c and λ are complex parameters such that c lies in the interior of a hyperbolic component of the Mandelbrot set but not at its center and λ is arbitrarily small. We prove that the Julia set of F λ consists of a countable collection of inverted copies of curves that are homeomorphic to the Julia set of F 0 and uncountably many point components that accumulate on each of these curves.