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Conjugacies for Tiling Dynamical Systems

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Abstract

We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being of finite type is invariant under topological conjugacy. For substitution tiling systems under rather general conditions, including the Penrose and pinwheel systems, we show that substitutions are invertible and that conjugacies are generalized sliding block codes.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas, Austin, TX, 78712, USA

    Charles Holton, Charles Radin & Lorenzo Sadun

Authors
  1. Charles Holton
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  2. Charles Radin
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  3. Lorenzo Sadun
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Additional information

Communicated by G. Gallavotti

Research supported in part by NSF Vigre Grant DMS-0091946

Research supported in part by NSF Grant DMS-0071643 and Texas ARP Grant 003658-158

Acknowledgement The authors are grateful for the support of the Banff International Research Station, at which we formulated and proved Theorem 3.

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Holton, C., Radin, C. & Sadun, L. Conjugacies for Tiling Dynamical Systems. Commun. Math. Phys. 254, 343–359 (2005). https://doi.org/10.1007/s00220-004-1195-3

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  • DOI: https://doi.org/10.1007/s00220-004-1195-3

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