A Characterization of Multiplicity-Preserving Global Bifurcations of Complex Polynomial Vector Fields
arXiv:1907.11999 · doi:10.1007/s12346-020-00424-y
Abstract
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 can be realized as a composition of a finite number of simpler bifurcations, and these bifurcations are characterized.
Revised exposition; results remain unchanged. Final version to appear in Qualitative Theory of Dynamical Systems