On the rate of convergence to the neutral attractor of a family of one-dimensional maps
Volume 206 / 2009
Fundamenta Mathematicae 206 (2009), 253-269
MSC: 37E05, 34D45, 90B80.
DOI: 10.4064/fm206-0-14
Abstract
For a family of maps $$ f_d(p)=1-(1-{p}/{d})^d, \quad\ d\in[2,\infty], \, p\in[0,1]. $$ 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.
