Metrics on trees I. The tower algorithm for interval maps
Metrics on trees I. The tower algorithm for interval maps
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树上的度量 I. 区间图的塔算法
DOI：
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发表时间：
2021
期刊：
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通讯作者：
G. Tiozzo
中科院分区：
文献类型：
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作者：
G. Tiozzo
我们认为米尔诺的塔算法在空间中的分段单调映射，迭代算法的度量空间的统一，一方面，瑟斯顿的迭代方案收敛到全纯模型，另一方面，理论的分段线性模型来自揉捏理论。我们证明了该算法收敛的单峰映射的高熵，并提供了例子，它不收敛的单峰映射的低熵和多模态映射的程度较高。
We consider Milnor’s tower algorithm in the space of piecewise monotone maps, an iterative algorithm on the space of metrics which unifies, on the one hand, Thurston’s iterative scheme which converges to holomorphic models, and, on the other hand, the theory of piecewise linear models coming from kneading theory. We prove that the algorithm converges for unimodal maps of high entropy, and provide examples where it does not converge for unimodal maps of low entropy and multimodal maps of higher degree.