Integrability of polynomial vector fields and a dual problem
Exactly Solvable and Integrable Systems
2024-11-22 v2 Classical Analysis and ODEs
Dynamical Systems
Abstract
We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality the case of quadratic vector fields is considered in detail.
Cite
@article{arxiv.2409.04322,
title = {Integrability of polynomial vector fields and a dual problem},
author = {Tatjana Petek and Valery Romanovski},
journal= {arXiv preprint arXiv:2409.04322},
year = {2024}
}