Conjugacies for Tiling Dynamical Systems

Abstract

We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being 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.

Updated to version accepted for publication

References in corpus (2)

• When size matters: subshifts and their related tiling spaces
• A Homeomorphism Invariant for Substitution Tiling Spaces

Cited by in corpus (6)

• Recognizability for sequences of morphisms
• Fusion: a general framework for hierarchical tilings of $R^d$
• PV cohomology of pinwheel tilings, their integer group of coinvariants and gap-labelling
• Admissible reversing and extended symmetries for bijective substitutions
• Cobham-Semenov theorem and $\NN^d$-subshifts
• Invariant measures for non-primitive tiling substitutions