Necessary conditions for existence of tensor invariants for general nonlinear dynamical systems
Dynamical Systems
2026-03-10 v1 Classical Analysis and ODEs
Abstract
The integrability has been playing an essential role in the field of differential equations. This property may better help us obtain the topological structure and even the global dynamics for the considered system. A system is called integrable if it has a number of tensor invariants, which can comprehensively define the integrability problem. In this paper, we give necessary conditions for existence of tensor invariants for general nonlinear systems, especially semi-quasihomogeneous systems. Our results may be viewed as a generalization of Poincar\'e and Kozlov's work.
Keywords
Cite
@article{arxiv.2603.07210,
title = {Necessary conditions for existence of tensor invariants for general nonlinear dynamical systems},
author = {Zitong Zhao and Shaoyun Shi and Wenlei Li and Zhiguo Xu and Kaiyin Huang},
journal= {arXiv preprint arXiv:2603.07210},
year = {2026}
}