First integrals and invariants of systems of ODEs
Dynamical Systems
2025-11-11 v1
Abstract
We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincar\'{e}-Dulac normal forms for autonomous systems of ODEs with diagonal matrix of the linear part. Using tools from computational algebra, we develop an algorithmic approach for identifying generators of the algebras of monomial and polynomial first integrals, which works in the general case where the matrix of the linear part includes algebraic complex eigenvalues. Our method also provides a practical tool for exploring the algebraic structure of polynomial invariants and their relation to the Poincar\'{e}-Dulac normal forms of the underlying vector fields.
Keywords
Cite
@article{arxiv.2507.22489,
title = {First integrals and invariants of systems of ODEs},
author = {Mateja Grašič and Abdul Salam Jarrah and Valery G. Romanovski},
journal= {arXiv preprint arXiv:2507.22489},
year = {2025}
}