Chapter 9 Holonomy and the Lotka–Volterra System
摘要
In this section we give another idea related to monodromy. This is the holonomy of the foliation P dy−Qdx = 0 associated to the system (1.2) in the neighborhood of an invariant curve. This object, roughly speaking, is the nonlinear analog to the monodromy of the solutions of a linear differential equation as they turn around a singular point. Alternatively, it can be thought of as a kind of Poincar´e return map for foliations.