The idea goes back to Jacques Hadamard's 1898 paper on the geodesics on surfaces of negative curvature.
[2] George Birkhoff, Norman Levinson and the pair Mary Cartwright and J. E. Littlewood have applied similar methods to qualitative analysis of nonautonomous second order differential equations.
A spectacular application of the methods of symbolic dynamics is Sharkovskii's theorem about periodic orbits of a continuous map of an interval into itself (1964).
[5] Symbolic dynamics originated as a method to study general dynamical systems; now its techniques and ideas have found significant applications in data storage and transmission, linear algebra, the motions of the planets and many other areas[citation needed].
Each state is associated with a symbol and the evolution of the system is described by an infinite sequence of symbols—represented effectively as strings.