English

Rank one Z^d actions and directional entropy

Dynamical Systems 2008-09-10 v2

Abstract

We study the directional entropy of rank one Z^d actions. We show that if the sequence of towers generating the action are rectangular in shape, then there is always a direction along which the directional entropy is zero. If the rectangles satisfy a "sub-exponential growth" condition, then we show that the directional entropy is zero in every direction.

Cite

@article{arxiv.0809.1626,
  title  = {Rank one Z^d actions and directional entropy},
  author = {E. Arthur Robinson and Ayse A. Sahin},
  journal= {arXiv preprint arXiv:0809.1626},
  year   = {2008}
}
R2 v1 2026-06-21T11:18:29.826Z