On the rate of convergence to the neutral attractor of a family of one-dimensional maps

For a family of maps (equation presented) we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point. © 2009 Instytut Matematyczny PAN.