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Topology of analytic foliations in \(\mathbb{C}^{2}\). The Kupka-Smale property. (English. Russian original) Zbl 1351.37198

Proc. Steklov Inst. Math. 254, 152-168 (2006); translation from Tr. Mat. Inst. Steklova 254, 162-180 (2006).
Summary: The topology of leaves of a generic analytic foliation on the complex plane is studied. It is proved that for a generic foliation all leaves are topological disks except for at most a countable number of topological cylinders. It is also shown that such foliations possess the Kupka-Smale property.

MSC:

37F75 Dynamical aspects of holomorphic foliations and vector fields
32S65 Singularities of holomorphic vector fields and foliations
37C20 Generic properties, structural stability of dynamical systems
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
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