On Julia sets of postcritically finite branched coverings Part I―coding of Julia sets

Atsushi KAMEYAMA

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On Julia sets of postcritically finite branched coverings Part I―coding of Julia sets

机译：关于临界后分支覆盖的Julia集第一部分-Julia集的编码

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We define Julia sets for (topological) expanding postcritically finite branched coverings on S~2, and show the existence and the uniqueness of Julia sets. Our main aim is the investigation of codings of Julia sets (i.e. semiconjugacies between symbolic dynamics and Julia sets). In particular, it is proved that if two expanding branched coverings are combinatorially equivalent, then their Julia sets are topologically conjugate.

机译：我们定义了S〜2上的（拓扑）后临界有限分支覆盖的Julia集，并显示了Julia集的存在性和唯一性。我们的主要目的是研究Julia集的编码（即符号动力学和Julia集之间的半共轭）。特别地，证明了如果两个扩展的分支覆盖在组合上是等效的，则它们的Julia集在拓扑上是共轭的。

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来源
《Journal of the Mathematical Society of Japan》 |2003年第2期|p.439-454|共16页
作者
Atsushi KAMEYAMA;
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作者单位

Department fo Informatics and Mathematical Science Graduate School fo Engineering Science Osaka University Machikaaneyama-cho 1-3 Toyonaka, Osaka 560-8531 Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
julia set; postcritically finite branched covering; thurston equivalence; symbolic dynamics; coding map; self-similar set; fundamental group;

机译：朱莉娅集后临界有限分支覆盖;瑟斯顿等值;符号动力学;编码图自相似集基本群体;

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机译：关于临界后分支覆盖的Julia集第二部分― Julia集的S〜1参数化
2. Structure of Julia sets of polynomial semigroups with bounded finite postcritical set [J] . Stankewitz R, Sumi H Applied mathematics and computation . 2007,第1期

机译：有界有限后临界集的多项式半群的Julia集的结构
3. Graphical exploration of the connectivity sets of alternated Julia sets: M, the set of disconnected alternated Julia sets [J] . Danca M.-F., Bourke P., Romera M. Nonlinear dynamics . 2013,第1a2期

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4. Laplacians on Julia Sets III: Cubic Julia Sets and Formal Matings [C] . Calum Spicer, Robert S. Strichartz, Emad Totari AMS Special Session on Fractal Geometry in Pure and Applied Mathematics in Memory of Benoit Mandelbrot;AMS Special Session on Geometry and Analysis on Fractal Spaces . 2013

机译：朱莉娅的拉普拉斯套装III：立方朱莉娅套和正式的果实
5. Computational complexity of Euclidean sets: Hyperbolic Julia sets are poly-time computable. [D] . Braverman, Mark. 2004

机译：欧几里得集的计算复杂度：双曲Julia集是可多次计算的。
6. An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves [O] . Yuanyuan Sun, Lina Chen, Rudan Xu, -1

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7. On Julia sets of postcritically finite branched coverings Part I--coding of Julia sets [O] . Atsushi KAMEYAMA 2003

机译：关于朱莉娅的后期有限分支覆盖物的第一部分我 - 朱莉娅套装编码

On Julia sets of postcritically finite branched coverings Part I―coding of Julia sets

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