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Extended holonomy and topological invariance of vanishing holonomy group. (English) Zbl 1203.32012
Summary: We introduce the notion of extended holonomy and discuss some of its properties. As an application of it, we consider vanishing projective holonomy groups of germs of vector fields with zero \((n - 1)\)-jet and prove, under some genericity assumptions, that the corresponding vanishing holonomy groups are topologically conjugated for orbitally topologically equivalent germs of vector fields.

MSC:
32S65 Singularities of holomorphic vector fields and foliations
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
37F75 Dynamical aspects of holomorphic foliations and vector fields
34C14 Symmetries, invariants of ordinary differential equations
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