On parameter space of complex polynomial vector fields in C

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Dias, Kealey¹  Lei, Tan² 

[1] CUNY, Bronx Community Coll, 2155 Univ Ave, Bronx, NY 10453 USA

[2] Univ Angers, Fac Sci, LAREMA, 2 Blvd Lavoisier, F-49045 Angers 01, France

关键词: Holomorphic foliation;    Holomorphic vector field;    Bifurcations;    Qualitative dynamics;    Abelian differential;    Quadratic differential;   

DOI  :  10.1016/j.jde.2015.09.001

来源: Elsevier

【 摘 要 】

The space Xi(d) 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. 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free