Statistical stability  for  multi-substitution tiling spaces

Rui Pacheco; Helder Vilarinho

doi:10.3934/dcds.2013.33.4579

Article Contents

2013, Volume 33, Issue 10: 4579-4594. Doi: 10.3934/dcds.2013.33.4579

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Statistical stability for multi-substitution tiling spaces

Rui Pacheco^1, and
Helder Vilarinho^1,

1.
Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, Covilhã, 6200-001

Received: June 30, 2012

Revised: December 31, 2012

Published: September 2013

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Abstract

Given a finite set $\{S_1\dots,S_k \}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\mathbb{R}^d$, we consider the multi-substitution tiling space associated to each sequence $\bar a\in \{1,\ldots,k\}^{\mathbb{N}}$. 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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Mathematics Subject Classification: Primary: 37A15, 37A25, 52C22.

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