Iterated Monodromy Groups
Iterated Monodromy Groups
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迭代单峰群
DOI：
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发表时间：
2003
期刊：
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通讯作者：
V. Nekrashevych
中科院分区：
文献类型：
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作者：
V. Nekrashevych
我们将一个群IMG（f）与拓扑空间M的每一个由其开子集构成的覆盖f相关联。它是基本群m（M）与其单值作用的核的交集的商。每一个迭代的单值群都在一棵有根树上有一个自然定义的动作。我们提出了一个有效的方法来计算这个行动，并显示如何动态的f是相关的组。特别地，如果f是扩张的，则f的Julia集可以从IMG（f）（从它在树上的作用）重构。
We associate a group IMG(f) to every covering f of a topological space M by its open subset. It is the quotient of the fundamental group �1(M) by the intersection of the kernels of its monodromy action for the iterates f n . Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamics of f is related to the group. In particular, the Julia set of f can be reconstructed from IMG(f) (from its action on the tree), if f is expanding.