English

Invariant Algebraic Surfaces and Constrained Systems

Dynamical Systems 2020-01-08 v1

Abstract

We study flows of smooth vector fields XX over invariant surfaces MM which are levels of rational first integrals. It leads us to study constrained systems, that is, systems with impasses. We identify a subset IM\mathcal{I} \subset M which we call "pseudo-impasse" set and analyze the flow of X by points of I\mathcal{I}. Systems well known in the literature exemplify our results: Lorenz, Chen, Falkner-Skan and Fisher-Kolmogorov. We also study 1-parameter families of integrable systems and unfolding of minimal sets. Our main tool is the geometric singular perturbation theory.

Keywords

Cite

@article{arxiv.2001.01741,
  title  = {Invariant Algebraic Surfaces and Constrained Systems},
  author = {Paulo Ricardo da Silva and Otávio Henrique Perez},
  journal= {arXiv preprint arXiv:2001.01741},
  year   = {2020}
}
R2 v1 2026-06-23T13:04:17.613Z