Invariant Algebraic Surfaces and Constrained Systems
Dynamical Systems
2020-01-08 v1
Abstract
We study flows of smooth vector fields over invariant surfaces which are levels of rational first integrals. It leads us to study constrained systems, that is, systems with impasses. We identify a subset which we call "pseudo-impasse" set and analyze the flow of X by points of . 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}
}