On dual surjunctivity and applications

We explore the dual version of Gottschalk’s conjecture recently introduced by Capobianco, Kari, and Taati, notion surjunctivity in general. show that surjunctive groups satisfy Kaplansky’s direct finiteness for all fields positive characteristic. By quantifying notions injectivity post-surjectivity cellular automata, we image full topological shift under an injective automaton is a subshift finite type quantitative way. Moreover, are closed ultraproducts, elementary equivalence, certain semidirect products (using ideas Arzhantseva Gal latter); they form subset space marked groups, fully residually surjunctive, etc. also consider systems more general dynamical systems, namely expansive algebraic actions, employing results Chung Li.