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This survey is the continuation of a series of works aimed at applying toolsfrom Singularity Theory to Differential Equations. More precisely, we utilizethe powerfull Milnor's Fibration Theory to give geometric-topologicalclassifications of first integrals of differential systems. In the previouspaper, systems of first-order quasilinear partial differential equations wereexamined, focusing on the case of an isolated singularity. Now, we address bothcases of isolated and \textit{non-isolated singularities} for more generaldynamical systems (namely, \textit{foliations}) that admit at least one firstintegral. For this, we utilize recently established connections betweenharmonic morphisms and Milnor fibrations to provide topological and geometricdescriptions of the foliations under consideration. In particular, we applythese results to analyze the graph of solutions of some quasilinear systems.

Topology of first integrals via Milnor fibrations II