Dynamics of A Re-Parametrization of A 2-Dimensional Mapping Derived from Double Discrete Sine-Gordon Mapping

Abstract

We study the dynamics of a two dimensional map which is derived from another two dimensional map by re-parametrizing the parameter in the system. It is shown that some of the properties of the original map can be preserved by the choice of the re-parametrization. By means of performing stability analysis to the critical points, and also studying the level set of the integrals, we study the dynamics of the re-parametrized map. Furthermore, we present preliminary results on the existence of a set where iteration starts at a point in that set, in which it will go off to infinity after finite step.

Keywords

• re-parametrizing
• 2-dimensional mapping
• generalized double discrete sine-gordon
• integral