In
mathematics,
symbolic dynamics is the practice of modeling a topological or smooth
dynamical system by a discrete space consisting of infinite
sequences of abstract symbols, each of which corresponds to a
state of the system, with the dynamics (evolution) given by the
shift operator. Formally, a
Markov partition is used to provide a
finite cover for the smooth system; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one covering set to another.