Author:
ARTHUR ROBINSON E.,ŞAHİN AYŞE A.
Abstract
AbstractWe study the dynamic properties of rank-one ℤd actions as a function of the geometry of the shapes of the towers generating the action. Some basic properties require only minimal restrictions on the geometry of the towers. Our main results concern the directional entropy of rank-one ℤd actions with rectangular tower shapes, where we show that the geometry of the rectangles plays a significant role. We show that for each n≤d there is an n-dimensional direction with entropy zero. We also show that if the growth in eccentricity of the rectangular towers is sub-exponential, then all directional entropies are zero. An example of D. Rudolph shows that, without a restriction on eccentricity, a positive entropy direction is possible.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献