Garden of Eden and Specification

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.

16 pages. Minor changes. To appear in ETDS

References in corpus (3)

• Amenability of groups is characterized by Myhill's Theorem
• A Garden of Eden theorem for principal algebraic actions
• The Garden of Eden theorem: old and new

Cited by in corpus (3)

• Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property
• Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity
• Homoclinically expansive actions and a Garden of Eden theorem for harmonic models