English

Complexity and directional entropy in two dimensions

Dynamical Systems 2014-09-18 v1

Abstract

We study the directional entropy of the dynamical system associated to a Z2\Z^2 configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a Z2\Z^2 system with the same local assumptions have zero directional entropy.

Keywords

Cite

@article{arxiv.1409.5056,
  title  = {Complexity and directional entropy in two dimensions},
  author = {Ryan Broderick and Van Cyr and Bryna Kra},
  journal= {arXiv preprint arXiv:1409.5056},
  year   = {2014}
}
R2 v1 2026-06-22T05:59:02.411Z