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- W4297782511 abstract "We describe the equivalence classes of germs of generic $2$-parameter families of complex vector fields $dot z = omega_epsilon(z)$ on $mathbb{C}$ unfolding a singular parabolic point of multiplicity $k+1$: $omega_0= z^{k+1} +o(z^{k+1})$. The equivalence is under conjugacy by holomorphic change of coordinate and parameter. As a preparatory step, we present the bifurcation diagram of the family of vector fields $dot z = z^{k+1} + epsilon_1 z + epsilon_0$ over $mathbb{CP}^1$. This presentation is done using the new tools of periodgon and star domain. We then provide a description of the modulus space and (almost) unique normal forms for the equivalence classes of germs." @default.
- W4297782511 created "2022-10-01" @default.
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- W4297782511 date "2017-10-02" @default.
- W4297782511 modified "2023-09-25" @default.
- W4297782511 title "Generic 2-parameter perturbations of parabolic singular points of vector fields in C" @default.
- W4297782511 doi "https://doi.org/10.48550/arxiv.1710.00883" @default.
- W4297782511 hasPublicationYear "2017" @default.
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