The theory had been developed by John Milnor and William Thurston in two widely circulated and influential Princeton preprints from 1977 that were revised in 1981 and finally published in 1988.
Applications of the theory include piecewise linear models, counting of fixed points, computing the total variation, and constructing an invariant measure with maximal entropy.
Kneading theory provides an effective calculus for describing the qualitative behavior of the iterates of a piecewise monotone mapping f of a closed interval I of the real line into itself.
Some quantitative invariants of this discrete dynamical system, such as the lap numbers of the iterates and the Artin–Mazur zeta function of f are expressed in terms of certain matrices and formal power series.
A closely related kneading determinant is a formal power series with odd integer coefficients.