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- W2337390929 abstract "We give normal forms for generic k -dimensional parametric families of germs of planar holomorphic vector fields unfolding a saddle-node singularity, under the condition that there exists a family of invariant analytic curves unfolding the weak separatrix of the saddle-node. These normal forms provide a moduli space for these parametric families. In our former 2008 paper, a modulus of a family was given as the unfolding of the Martinet-Ramis modulus, but the realization part was missing. We solve the realization problem in that partial case and show the equivalence between the two presentations of the moduli space. Finally, we completely characterize the families which have a modulus depending analytically on the parameter." @default.
- W2337390929 created "2016-06-24" @default.
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- W2337390929 date "2021-01-01" @default.
- W2337390929 modified "2023-09-26" @default.
- W2337390929 title "Analytic Normal forms and inverse problems for unfoldings of 2-dimensional saddle-nodes with analytic center manifold" @default.
- W2337390929 doi "https://doi.org/10.24033/asens.2457" @default.
- W2337390929 hasPublicationYear "2021" @default.
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