论文标题
不变的代数表面和受约束的系统
Invariant Algebraic Surfaces and Constrained Systems
论文作者
论文摘要
我们研究了平滑矢量场的流量$ x $，而不是不变的表面$ m $，这是理性第一积分的水平。它导致我们研究受障碍的受限系统。我们确定一个子集$ \ MATHCAL {I} \子集M $，我们称之为“ pseudo-impasse”设置，并通过$ \ Mathcal {i} $的点分析x的流程。文献中众所周知的系统体现了我们的结果：Lorenz，Chen，Falkner-Skan和Fisher-Kolmogorov。我们还研究了1-参数的综合系统和最小套装的群体。我们的主要工具是几何奇异扰动理论。
We study flows of smooth vector fields $X$ over invariant surfaces $M$ which are levels of rational first integrals. It leads us to study constrained systems, that is, systems with impasses. We identify a subset $\mathcal{I} \subset M$ which we call "pseudo-impasse" set and analyze the flow of X by points of $\mathcal{I}$. 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.
