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arXiv · 1207.3693

Statistical Stability for Multi-Substitution Tiling Spaces

Rui Pacheco·Helder Vilarinho
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Abstract

Given a finite set ${S_1...,S_k}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\rd$, we consider the multi-substitution tiling space associated to each sequence $\bar a\in {1,...,k}^{\mathbb{N}}$. The action by translations on such spaces gives rise to uniquely ergodic dynamical systems. In this paper we investigate the rate of convergence for ergodic limits of patches frequencies and prove that these limits vary continuously with $\bar a$.

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Rui Pacheco, Helder Vilarinho. 2012-07-16. Statistical Stability for Multi-Substitution Tiling Spaces. https://arxiv.org/abs/1207.3693

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