On Parameter Space of Complex Polynomial Vector Fields in the Complex Plane
Abstract
The space of degree d single-variable monic and centered complex polynomial vector fields can be decomposed into loci in which the vector fields have the same topological structure. We analyze the geometric structure of these loci and describe some bifurcations, in particular, it is proved that new homoclinic separatrices can form under small perturbation. By an example, we show that this decomposition of parameter space by combinatorial data is not a cell decomposition. The appendix to this article, joint work with Tan Lei, shows that landing separatrices are stable under small perturbation of the vector field if the multiplicities of the equilibrium points are preserved.
Cite
@article{arxiv.1406.4117,
title = {On Parameter Space of Complex Polynomial Vector Fields in the Complex Plane},
author = {Kealey Dias and Lei Tan},
journal= {arXiv preprint arXiv:1406.4117},
year = {2014}
}
Comments
28 pages, 17 figures; Appendix by Kealey Dias, Lei Tan. arXiv admin note: text overlap with arXiv:1007.5003