Non-linear Analytic Differential Equations and Their Invariants

Leonardo Meireles Câmara

Keywords: holomorphic foliations | holonomy | resolution of singularities

We study the classification of analytic differential equations in $(\bf{C}^{2},0)$ with finitely many separatrices. We give a complete set of analytic invariants determining the analytic type of a generic case (generalized curves). We define the notion of simple resolution foliation. With some conditions on the holonomy and the separatrix set we study the topological and analytic types of generalized curves with simple resolution.

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