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- W3100542760 abstract "When a singular point of a vector field passes through resonance, a formal invariant cone appears. In the seventies, Pyartli proved that for $(-1,1)$-resonance the cone is in fact analytic and is the degeneration of a family of invariant cylinders. In his thesis, Stolovitch established a new type of normal form and proved that for a simple resonance and under arithmetic conditions the cone is (the germ of) an analytic variety. In this paper, we prove a versal deformation theorem for analytic vector fields with an isolated singularity over Cantor sets. Our result implies that, under arithmetic conditions, the resonant cone is the degeneration of a set of invariant manifolds like in Pyartli's example. For the multi-Hopf bifurcation, that is for the $(-1,1)^d$-resonance, this implies the existence of vanishing tori carrying quasi-periodic motions generalising previous results of Chenciner and Li." @default.
- W3100542760 created "2020-11-23" @default.
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- W3100542760 date "2020-11-13" @default.
- W3100542760 modified "2023-09-27" @default.
- W3100542760 title "Versal deformations of vector field singularities" @default.
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