Dynamic classification of escape time Sierpinski curve Julia sets
Dynamic classification of escape time Sierpinski curve Julia sets
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DOI：
10.4064/fm202-2-5
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发表时间：
2009
影响因子：
0.6
通讯作者：
R. Devaney;K. Pilgrim
中科院分区：
文献类型：
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作者：
R. Devaney;K. Pilgrim
对于 n ≥ 2，有理映射族 Fλ(z) = z + λ/z 包含可数无限组参数值，其中所有临界轨道在经过一定次数 κ 的迭代后最终落在无穷远点上。如果 κ ≥ 3，此类映射的 Julia 集就是谢尔宾斯基曲线。我们证明，当且仅当两个此类映射是莫比乌斯共轭或反莫比乌斯共轭时，两个此类映射在其 Julia 集上是拓扑共轭的，并且我们给出了作为 n 和 κ 函数的拓扑共轭类数量的精确计数。
For n ≥ 2, the family of rational maps Fλ(z) = z + λ/z contains a countably infinite set of parameter values for which all critical orbits eventually land after some number κ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if κ ≥ 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and κ.