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A characterization of multiplicity-preserving global bifurcations of complex polynomial vector fields. (English) Zbl 07273483
Summary: For the space of single-variable monic and centered complex polynomial vector fields of arbitrary degree \(d\), it is proved that any bifurcation which preserves the multiplicity of equilibrium points admits a decomposition into a finite number of elementary bifurcations, and the elementary bifurcations are characterized.
MSC:
37F46 Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37F75 Dynamical aspects of holomorphic foliations and vector fields
32M25 Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions
34C23 Bifurcation theory for ordinary differential equations
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