turkmath.org

The Garden of Eden theorem was established by Edward Moore and John Myhill in 1963. It states that a cellular automaton is surjective if and only if it satisfies a weak form of injectivity known as pre-injectivity. In 1999, Mikhail Gromov suggested that the Garden of Eden theorem could be extended to a suitable class of hyperbolic dynamical systems. In this talk, I will discuss the classical Garden of Eden theorem as well as some recent results in the direction indicated by Gromov. This is joint work with Tullio Ceccherini-Silberstein.