A Characterization of Rotation Number on One-Dimensional Tiling Spaces
Dynamical Systems
2017-08-14 v2
Abstract
Identity-homotopic self-homeomorphisms of a space of non-periodic 1-dimensional tiling are generalizations of orientation-preserving self-homeomorphisms of circles. We define the analogue of rotation numbers for such maps. In constrast to the classical situation, additional assumptions are required to make rotation numbers globally well-defined and independent of initial conditions. We prove that these conditions are sufficient, and provide counterexamples when these conditions are not met.
Keywords
Cite
@article{arxiv.1708.00901,
title = {A Characterization of Rotation Number on One-Dimensional Tiling Spaces},
author = {Betseygail Rand and Lorenzo Sadun},
journal= {arXiv preprint arXiv:1708.00901},
year = {2017}
}
Comments
Many of the results in this paper had previously appeared in papers by A. Clark, by Y. Shvestov, and by J. Aliste-Prieto