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arXiv · 1708.09012

Garden of Eden and Specification

Hanfeng Li
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Abstract

We establish a Garden of Eden theorem for expansive algebraic actions of amenable groups with the weak specification property, i.e. for any continuous equivariant map T from the underlying space to itself, T is pre-injective if and only if it is surjective. In particular, this applies to all expansive principal algebraic actions of amenable groups and expansive algebraic actions of Z^d with CPE.

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Hanfeng Li. 2017-08-29. Garden of Eden and Specification. https://doi.org/10.1017/etds.2018.6

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