On Parameter Space of Complex Polynomial Vector Fields in C - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

On Parameter Space of Complex Polynomial Vector Fields in C

Abstract

The space Ξd of degree d single-variable monic and centered complex polyno- mial vector fields can be decomposed into loci in which the vector fields have the same topological structure. This paper analyzes the geometric structure of these loci and describes 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.
Fichier principal
Vignette du fichier
KealeyDias_ParameterSpace_LandingStable_withTanLei_JofDiffEq.pdf (1.59 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01027414 , version 1 (28-05-2015)

Identifiers

  • HAL Id : hal-01027414 , version 1

Cite

Kealey Dias, Lei Tan. On Parameter Space of Complex Polynomial Vector Fields in C. 2014. ⟨hal-01027414⟩
98 View
99 Download

Share

Gmail Facebook Twitter LinkedIn More