Back to Search
Start Over
Realization problems for limit cycles of planar polynomial vector fields
- Source :
- Journal of Differential Equations, 260 (2015) 4
- Publication Year :
- 2015
-
Abstract
- We show that for any finite configuration of closed curves $\Gamma\subset \mathbb{R}^2$, 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.<br />Comment: 14 pages. New version: included extra references
- Subjects :
- Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Differential Equations, 260 (2015) 4
- Publication Type :
- Report
- Accession number :
- edsarx.1507.00698
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jde.2015.10.044