Factoring onto ${\mathbb{Z}}^d$ subshifts with the finite extension property

Abstract

We define the finite extension property for $d$-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined by Briceño (2016), and we prove that this property is invariant under topological conjugacy. Moreover, we prove that for every $d$, every $d$-dimensional block gluing subshift factors onto every $d$-dimensional subshift which has strictly lower entropy, a fixed point, and the finite extension property. This result extends a theorem from Boyle, Pavlov, and Schraudner (2010), which requires that the factor contain a safe symbol.

arXiv comment16 pages, 4 figures. Acknowledgments added in this version

Cited by in corpus (1)

• Factor maps and embeddings for random ${\mathbb{Z}}^d$ shifts of finite type