The search for Invariants for 3D Systems of 1ODEs - a new Method and Integrability Analysis

2017/08/29 by L. G. S. Duarte, L.G.S. Duarte, Duarte, L. G. S. +6
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1708.08893

10 pages

arxiv created 2017/08/29 · openalex publication_date 2017/08/29 · arxiv updated 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce new theoretical results that will lead to a novel, more efficient, approach to determine these invariants. Furthermore, one important aspect of such dynamical systems is that the integrability can be an issue. We will show that the present theoretical development allows for an Integrability analysis in the case where the system has free parameters.

Related

• Integrability of the one dimensional Schroedinger equation
• Solving first order differential equations presenting elementary functions
• Fundamental invariants of systems of ODEs of higher order
• Nilpotent integrability, reduction of dynamical systems and a third-order Calogero-Moser system
• Integrable Hamiltonian Hierarchies and Lagrangian 1-Forms