Multidimensional Discrete Dynamical Systems with Slow Behavior

Abstract

In this work we state sufficient conditions for convergence for nonhyperbolic fixed points of multidimensional discrete dynamical systems and analyze their speed of convergence. We introduce a new concept of slow convergence based on one dimensional discrete systems and we establish a general classification for slow discrete dynamical systems which is of paramount importance in numerical analysis and in the development of algorithms. A variety of two dimensional examples are presented to illustrate the diverse possibilities of convergence existing in multidimensional systems.