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, Sturman, Substitutive And Toeplitz Subshifts, And Cellular Automata.--jacket. Dynamical Systems -- Topological Dynamics -- Symbolic Dynamics -- Minimal Symbolic Systems -- Cellular Automata. Petr Kůrka. Includes Bibliographical References (p. [297]-306) And Index.