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arXiv · 1611.03570

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

Raimundo Briceño·Kevin McGoff·Ronnie Pavlov
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Abstract

We define the finite extension property for $d$-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined by Brice\~no (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.

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Raimundo Briceño, Kevin McGoff, Ronnie Pavlov. 2016-11-11. Factoring onto $\mathbb{Z}^d$ subshifts with the finite extension property. https://arxiv.org/abs/1611.03570

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