Reversible D-Dimensional CA Over the Ring ZM and Some Applications in Ergodic Theory

Explore the intricacies of cellular automata (CA) and their applications in ergodic theory in this 59-minute seminar by Hasan AKIN from ICTP Mathematics. Delve into 1-dimensional CA on the field $\mathbf{Z}_p$ and ring $\mathbf{Z}_m$, examining their ergodic properties and entropies. Investigate the invertibility of 1DLCA generated linear local rules over $\mathbf{Z}_{m}$ and study the ergodic theory of infinite linear CA with respect to Bernoulli and Markov measures. Learn about measure-theoretic entropy and its calculation using the Kolmogorov-Sinai Theorem. Discover the concept of topological entropy for continuous maps on compact metric spaces, focusing on 1D LCA over $\mathbb{Z}_m^{\mathbb{Z}}$. Examine directional measure-theoretic entropy of $\mathbb{Z}^{2}$-actions generated by shift maps and 1D-CA, and explore topological directional entropy algorithms for $\mathbb{Z}^{2}$-actions.