标题： 关于具有一阶独立首次积分的参数化动力系统平衡点集 显示英文标题

标题： On the Equilibrium Locus of a Parameterized Dynamical System with Independent First Integrals

摘要： 对于欧几里得空间的一个紧致区域中具有$k > 0$个独立首次积分的动力系统族，我们研究了平衡点流形。 我们证明，在温和且一般的条件下，它是一个光滑流形，可以被视为某个纤维丛的全空间，并且该纤维丛自然地配备了一个联络。 然后我们继续证明此联络下的平行移动确实存在，并探讨其一些性质。 特别是，我们阐明了如何在一定程度上度量系统特征值在给定纤维上的变化情况。 显示英文摘要

摘要： For a family of dynamical systems with $k > 0$ independent first integrals evolving in a compact region of an Euclidean space, we study the equilibrium locus. We show that under mild and generic conditions, it is a smooth manifold that can be viewed as the total space of a certain fiber bundle and that this bundle comes equipped with a natural connection. We then proceed to show parallel transport for this connection does exist and explore some of its properties. In particular, we elucidate how one can to some extent measure the variation of the system eigenvalues restricted to a given fiber.