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

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...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 52; no. 31; pp. 31 - 41
Main Authors Celledoni, E, Evripidou, C, McLaren, D I, Owren, B, Quispel, G R W, Tapley, B K, van der Kamp, P H
Format Journal Article
LanguageEnglish
Published IOP Publishing 02.08.2019
Subjects
Darboux polynomials
first integrals
rational maps
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Summary: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.
Bibliography:JPhysA-111205.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab294b