Self-Similarity for the Tricorn
Self-Similarity for the Tricorn
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DOI：
10.1080/10586458.2017.1420502
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发表时间：
2014-11
影响因子：
0.5
通讯作者：
H. Inou
中科院分区：
文献类型：
--
作者：
H. Inou
摘要讨论了三角形的自相似性，反全纯二次族的连通性轨迹。作为Kiwi和作者[IK 12]对拉直映射研究的直接结果，我们证明了Mandelbrot集有许多同胚副本。借助于严格的数值计算，我们还证明了对于以飞机为中心的“婴儿三角”候选，拉直映射是不连续的，因此不是同胚映射。
ABSTRACT We discuss self-similar property of the tricorn, the connectedness locus of the anti-holomorphic quadratic family. As a direct consequence of the study on straightening maps by Kiwi and the author [IK 12], we show that there are many homeomorphic copies of the Mandelbrot sets. With the help of rigorous numerical computation, we also prove that the straightening map is not continuous for the candidate of a “baby tricorn” centered at the airplane, hence not a homeomorphism.