On Periodic Decompositions and Nonexpansive Lines
Dynamical Systems
2022-04-15 v1
Abstract
In his Ph.D. thesis, Michal Szabados conjectured that for a not fully periodic configuration with a minimal periodic decomposition the nonexpansive lines are exactly the lines that contain a period for some periodic configuration in such decomposition. In this paper, we study Szabados's conjecture. First, we show that we may consider a minimal periodic decomposition where each periodic configuration is defined on a finite alphabet. Then we prove that Szabados's conjecture holds for a wide class of configurations, which includes all not fully periodic low convex pattern complexity configurations.
Cite
@article{arxiv.2204.06658,
title = {On Periodic Decompositions and Nonexpansive Lines},
author = {Cleber Fernando Colle},
journal= {arXiv preprint arXiv:2204.06658},
year = {2022}
}
Comments
13 pages. arXiv admin note: text overlap with arXiv:1909.08195