Iterative functional equation \(x(x(t))= f(t)\) with \(f(t)\) piecewise linear
The author offers qualitative properties and algorithms for determining iterative square roots (1/2-th iterates) of piecewise linear functions [for general theory of iterative roots see e.g. \textit{M. Kuczma, B. Choczewski} and \textit{R. Ger}, Cambridge University Press (1990; Zbl 0703.39005), chapter 11]. Iterative square roots of linear functions and of continuous functions consisting of two linear pieces get rather detailed treatment, those of functions consisting of more linear pieces are described more briefly.
scientific article; zbMATH DE number 1423327