Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits (Q1862333)

For an algorithm finding not necessarily stable periodic points of discrete dynamical systems in Euclidean space -- developed by Davidchack and Lai -- the authors give a rigorous proof of convergence and prove at least quadratic convergence. The algorithm is a modified Newton method which constitutes an almost implicit Euler method for a related differential equation, and contains sufficient parameters for adjustment to be applied to special cases in a flexible way, e.g. stabilizing the target points. A discussion of examples is included.