Pierre Guillon

Symbolic Dynamics

I could more or less talk about (probably only part of):

motivations of symbolic dynamics, coding.
one-dimensional SFTs and sofic subshifts representation by graphs link with language theory or linear algebra. entropy, topological properties, ergodic properties.
one-dimensional substitutive systems minimality, S-adic systems, sturmian systems.
two-dimensional SFTs and sofic subshifts representation by Wang tilings embedding of Turing machines aperiodic tilings.
two-dimensional substitutive subshifts realization as sofic subshifts S-adic systems, effectively S-adic systems realization of entropies or effective subactions.
cellular automata, expansive directions in subshifts.
subshifts over groups (Cayley graphs) amenability, soficity of groups effective groups.