Realization problems for limit cycles of planar polynomial vector fields Articles uri icon

publication date

  • February 2016

start page

  • 3844

end page

  • 3859


  • 4


  • 260

International Standard Serial Number (ISSN)

  • 0022-0396

Electronic International Standard Serial Number (EISSN)

  • 1090-2732


  • 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.


  • limit cycle; polynomial vector field; integrating factor; realization problem; configurations; existence; systems