- Publ. Mat.
- Volume 63, Number 1 (2019), 105-123.
Topological classification of limit periodic sets of polynomial planar vector fields
We characterize the limit periodic sets of families of algebraic planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere of dimension 0 or 1. Conversely, we show that any compact and connected semialgebraic set of the sphere of dimension 0 or 1 can be realized as a limit periodic set.
Publ. Mat., Volume 63, Number 1 (2019), 105-123.
Received: 2 March 2017
Revised: 16 October 2017
First available in Project Euclid: 7 December 2018
Permanent link to this document
Digital Object Identifier
Primary: 34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) 34C08: Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
Secondary: 14P10: Semialgebraic sets and related spaces 37G15: Bifurcations of limit cycles and periodic orbits
Belotto da Silva, André; Espín Buendía, Jose Ginés. Topological classification of limit periodic sets of polynomial planar vector fields. Publ. Mat. 63 (2019), no. 1, 105--123. doi:10.5565/PUBLMAT6311903. https://projecteuclid.org/euclid.pm/1544151632