Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps

Abstract

In this letter we propose a systematic approach for detecting and calculating integrals and preserved measures of rational maps. The approach is based on the use of cofactors and discrete Darboux polynomials and relies on the use of symbolic algebra tools. We show, in three examples, how to use this method to detect and determine integrals and preserved measures of the considered rational maps.