Convergence on Two Dimensional 1-Slow Discrete Dynamical Systems

Abstract

In this work we give sufficient and necessary conditions for convergence for nonhyperbolic fixed points of two dimensional 1-slow discrete dynamical systems. To achieve this goal, we introduce two angular functions that play the role of the iteration derivatives for one dimensional discrete systems. We also discuss the convergence on different regions of the two dimensional phase space, including the quadrants. In this case, sufficient convergence conditions are given. Several two dimensional examples are presented to illustrate the use of the previous results.