共轭条件下揉捏矩阵的不变性

Pub Date : 2021-01-01 DOI:10.4134/JKMS.J190378

C. Gopalakrishna, Murugan Veerapazham

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引用次数: 0

摘要

。在Milnor和Thurston提出的揉捏理论中，证明了与连续块单调映射相关的揉捏矩阵和揉捏行列式在保向共轭条件下是不变的。研究了方向反转共轭问题，证明了方向反转共轭不是不变量，而方向反转共轭是不变量。并将所得结果应用于捏合矩阵的计算复杂度和映射的分类直至拓扑共轭。

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INVARIANCE OF KNEADING MATRIX UNDER CONJUGACY

. In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant as- sociated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classiﬁcation of maps up to topological conjugacy.

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