Topological and Symbolic Dynamics

A dynamical system is a continuous self-map of a compact metric space. Topological dynamics studies the iterations of such a map, or equivalently the trajectories of points of the state space. The basic concepts of topological dynamics are: minimality, transitivity, recurrence, shadowing property, stability, equicontinuity, sensitivity, attractors and topological entropy. Symbolic dynamics studies dynamical systems whose state spaces are zero-dimensional and consist of sequences of symbols. The main classes of symbolic dynamical systems are: adding machines, subshifts of finite type, sofic subshifts, Sturmian, substitutive and Toeplitz subshifts, and cellular automata. Key words: Topological dynamics, symbolic dynamics, subshifts, cellular automata, recurrence, transitivity, attractors, entropy Class. math. : 54H20, 34C35, 22C05, 34D45, 58F39