scholarly journals The Multiplicative Golden Mean Shift Has Infinite Hausdorff Measure

Author(s):  
Yuval Peres ◽  
Boris Solomyak
2017 ◽  
Vol 39 (5) ◽  
pp. 1234-1260
Author(s):  
JUNG-CHAO BAN ◽  
WEN-GUEI HU ◽  
SONG-SUN LIN

This study investigates a multiplicative integer system, an invariant subset of the full shift under the action of the semigroup of multiplicative integers, by using a method that was developed for studying pattern generation problems. The spatial entropy and the Minkowski dimensions of general multiplicative systems can thus be computed. A coupled system is the intersection of a multiplicative integer system and the golden mean shift, which can be decoupled by removing the multiplicative relation set and then performing procedures similar to those applied to a decoupled system. The spatial entropy can be obtained after the remaining error term is shown to approach zero.


2011 ◽  
Vol 349 (11-12) ◽  
pp. 625-628 ◽  
Author(s):  
Richard Kenyon ◽  
Yuval Peres ◽  
Boris Solomyak

2010 ◽  
Vol 29 (12) ◽  
pp. 3332-3335 ◽  
Author(s):  
Cun-wei TIAN ◽  
Guang-ying GE ◽  
Zhe SHEN

2009 ◽  
Vol 29 (8) ◽  
pp. 2074-2076
Author(s):  
Hua LI ◽  
Ming-xin ZHANG ◽  
Jing-long ZHENG

2009 ◽  
Vol 29 (6) ◽  
pp. 1680-1682
Author(s):  
Chang-tao CHEN ◽  
Qin ZHU ◽  
Sheng-yi ZHOU ◽  
Jia-ming ZHANG

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