符号动力学是数学中研究符号动力系统的学科。在符号动力系统中，系统的状态可以表示成有限个抽象符号的无穷串行，由任一状态点的运动轨迹可以通过简单的移位规则来确定。

关于符号动力学的起源可以追溯到雅克·阿达马在1898年的论文。

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.