Infinite Kneading Matrices and Weighted Zeta Functions of Interval Maps
Infinite Kneading Matrices and Weighted Zeta Functions of Interval Maps
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区间图的无限揉捏矩阵和加权Zeta函数
DOI：
10.1006/jfan.1995.1029
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发表时间：
1995
影响因子：
1.7
通讯作者：
V. Baladi
中科院分区：
文献类型：
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作者：
V. Baladi
摘要考虑一类分段连续、分段单调区间映射及其有界变差权、同调不变和周期点处连续。利用这些数据，我们将一系列加权的米尔诺-瑟斯顿捏合矩阵联系起来，收敛到一个具有系数解析函数的可数矩阵。我们证明了这些矩阵的行列式收敛到映射的相应加权Zeta函数的逆。作为推论，我们得到了马尔可夫区间映射、分段扩张区间映射和分段C1+BV区间映射的分段线性逼近的Perron-Frobenius算子的离散谱的收敛性质。
Abstract We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coefficients analytic functions. We show that the determinants of these matrices converge to the inverse of the correspondingly weighted zeta function for the map. As a corollary, we obtain convergence of the discrete spectrum of the Perron-Frobenius operators of piecewise linear approximations of Markovian, piecewise expanding, and piecewise C 1+ BV interval maps.
DOI：
--
发表时间：
1984
期刊：
--
影响因子：
--
作者：
M. Wodzicki
通讯作者：
M. Wodzicki