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 preserved measures and integrals of a rational map. The approach is based on the use of cofactors and Discrete Darboux Polynomials and relies on the use of symbolic algebra tools. Given sufficient computing power, all rational preserved integrals can be found. We show, in two examples, how to use this method to detect and determine preserved measures and integrals of the considered rational maps.

8 pages, 1 Figure

References in corpus (5)

• Geometric properties of Kahan's method
• Singularity, complexity, and quasi--integrability of rational mappings
• On integrability of Hirota-Kimura type discretizations
• Integrability properties of Kahan's method
• Duality for discrete integrable systems II

Cited by in corpus (5)

• Coalgebra symmetry for discrete systems
• An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps
• On tensor invariants of the Clebsch system
• Generating a chain of maps which preserve the same integral as a given map
• Kahan-Hirota-Kimura maps preserving original cubic hamiltonians