Holonomy and the Lotka-Volterra System

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)


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 Poincaré return map for foliations.


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© Birkhäuser Verlag 2007

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