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

Offered By: ICTP Mathematics via YouTube

Tags

Cellular Automata Courses Entropy Courses Ergodic Theory Courses

Course Description

Overview

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.

Syllabus

Reversible $d$-dmensional CA over the ring $\mathbb{Z}_m$ and some applications in ergodic theory


Taught by

ICTP Mathematics

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