Spectral measure of the Thue-Morse sequence and the dynamical system and random walk related to it
Spectral measure of the Thue-Morse sequence and the dynamical system and random walk related to it
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Thue-Morse 序列的谱测度以及与之相关的动力系统和随机游走
DOI：
10.1017/etds.2014.121
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发表时间：
2016
影响因子：
0.9
通讯作者：
Teturo Kamae and Li Peng
中科院分区：
文献类型：
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作者：
Mari Okada;S.Ponnusamy;A.Vasudevarao;Hiroshi Yanagihara;Kenjiro Yanagi;Kenjiro Yanagi;柳研二郎;Kenjiro Yanagi;Kenjiro Yanagi;Hiroshi Yanagihara;Kenjiro Yanagi;Mari Okada;Kohei Sekikawa;加藤幹雄，柳研二郎，三谷健一，高橋泰嗣;Teturo Kamae & Yu-Mei Xue;Teturo Kamae and Li Peng
log 2= 0.64298.... 在 [0, 1) 上的谱测量 µ 下，考虑变换 T，其中 T x= 2x (mod 1)。它被证明是 Kolmogorov 类型，熵至少为 D2 log 2。此外，随机游走由 T− 1 定义，其转移概率为 P1 ((1/2) x+(1/2) j| x)=(1/2)(1− cos (π (x+ j)))(j= 0, 1)。证明了这种随机游走是混合的并且μ是唯一的平稳测度。而且，林
log 2= 0.64298.... Under its spectral measure µ on [0, 1), consider the transformation T with T x= 2x (mod 1). It is shown to be of Kolmogorov type having entropy at least D2 log 2. Moreover, a random walk is defined by T− 1 which has the transition probability P1 ((1/2) x+(1/2) j| x)=(1/2)(1− cos (π (x+ j)))(j= 0, 1). It is proved that this random walk is mixing and µ is the unique stationary measure. Moreover, lim