Garden of Eden and specification

Hanfeng Li
SUNY Buffalo

A set is finite if and only if for every map from the set to itself surjectivity is equivalent to injectivity. The Garden of Eden theorem, or Moore-Myhill property, for a dynamical system refers to the equivalence between surjectivity and certain weak form of injectivity for every equivariant continuous map from the underlying space to itself. I will present a general GOE theorem for algebraic actions of amenable groups.

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