Algebraic limit cycles for quadratic polynomial differential systems

Jaume Llibre; Claudia Valls

doi:10.3934/dcdsb.2018070

Article Contents

2018, Volume 23, Issue 6: 2475-2485. Doi: 10.3934/dcdsb.2018070

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Algebraic limit cycles for quadratic polynomial differential systems

Jaume Llibre^1, , and
Claudia Valls^2,

1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
2.
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal

* Corresponding author: Jaume Llibre
* Corresponding author: Jaume Llibre

Received: July 2017

Early access: January 2018

Published: June 2018

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Abstract

We prove that for a quadratic polynomial differential system having three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, has at most one algebraic limit cycle. Our result provides a partial positive answer to the following conjecture: Quadratic polynomial differential systems have at most one algebraic limit cycle.

Keywords:

Algebraic limit cycle,
quadratic polynomial differential system,
quadratic polynomial vector field.

Mathematics Subject Classification: Primary: 37D99.

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References

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