Realization problems for limit cycles of planar polynomial vector fields

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Margalef-Bentabol, Juan^1,2  Peralta-Salas, Daniel³ 

[1] CSIC, Inst Estruct Mat, Madrid 28006, Spain

[2] Univ Carlos III Madrid, Grp Modelizac & Simulac Numer, Inst Gregorio Millan, Leganes 28911, Spain

[3] CSIC, Inst Ciencias Matemat, Madrid 28049, Spain

关键词: Limit cycle;    Polynomial vector field;    Integrating factor;    Realization problem;   

DOI  :  10.1016/j.jde.2015.10.044

来源: Elsevier

【 摘 要 】

We show that for any finite configuration of closed curves Gamma subset of R-2, one can construct an explicit planar polynomial vector field that realizes Gamma, up to homeomorphism, as the set of its limit cycles with prescribed periods, multiplicities and stabilities. The only obstruction given on this data is the obvious compatibility relation between the stabilities and the parity of the multiplicities. The constructed vector fields are Darboux integrable and admit a polynomial inverse integrating factor. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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