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arXiv · 1708.00901

A Characterization of Rotation Number on One-Dimensional Tiling Spaces

Betseygail Rand·Lorenzo Sadun
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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.

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Betseygail Rand, Lorenzo Sadun. 2017-08-02. A Characterization of Rotation Number on One-Dimensional Tiling Spaces. https://arxiv.org/abs/1708.00901

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