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.
Document type :
Preprints, Working Papers, ...
Liste complète des métadonnées

Cited literature [7 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01027414
Contributor : Lei Tan <>
Submitted on : Thursday, May 28, 2015 - 2:52:28 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM
Document(s) archivé(s) le : Monday, September 14, 2015 - 5:40:52 PM

File

KealeyDias_ParameterSpace_Land...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01027414, version 1

Collections

Citation

Kealey Dias, Lei Tan. On Parameter Space of Complex Polynomial Vector Fields in C. 2014. 〈hal-01027414〉

Share

Metrics

Record views

106

Files downloads

65