2019 Topological classification of limit periodic sets of polynomial planar vector fields
André Belotto da Silva, Jose Ginés Espín Buendía
Publ. Mat. 63(1): 105-123 (2019). DOI: 10.5565/PUBLMAT6311903

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.

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André Belotto da Silva. Jose Ginés Espín Buendía. "Topological classification of limit periodic sets of polynomial planar vector fields." Publ. Mat. 63 (1) 105 - 123, 2019. https://doi.org/10.5565/PUBLMAT6311903

Information

Received: 2 March 2017; Revised: 16 October 2017; Published: 2019
First available in Project Euclid: 7 December 2018

zbMATH: 07040963
MathSciNet: MR3908788
Digital Object Identifier: 10.5565/PUBLMAT6311903

Subjects:
Primary: 34C07 , 34C08
Secondary: 14P10 , 37G15

Keywords: limit periodic sets , ordinary differential equations , semi-algebraic sets

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.63 • No. 1 • 2019
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