Publicacions Matemàtiques

Topological classification of limit periodic sets of polynomial planar vector fields

André Belotto da Silva and Jose Ginés Espín Buendía

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Abstract

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.

Article information

Source
Publ. Mat., Volume 63, Number 1 (2019), 105-123.

Dates
Received: 2 March 2017
Revised: 16 October 2017
First available in Project Euclid: 7 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.pm/1544151632

Digital Object Identifier
doi:10.5565/PUBLMAT6311903

Subjects
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

Keywords
limit periodic sets ordinary differential equations semi-algebraic sets

Citation

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


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