Algebraic limit cycles for quadratic polynomial differential systems

Jaume Llibre; Claudia Valls

doi:10.3934/dcdsb.2018070

Algebraic limit cycles for quadratic polynomial differential systems

Jaume Llibre, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

© 2018 American Institute of Mathematical Sciences. All Rights Reserved. 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.

Original language	English
Pages (from-to)	2475-2485
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	23
Issue number	6
DOIs	https://doi.org/10.3934/dcdsb.2018070
Publication status	Published - 1 Aug 2018

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title = "Algebraic limit cycles for quadratic polynomial differential systems",

abstract = "{\textcopyright} 2018 American Institute of Mathematical Sciences. All Rights Reserved. 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.",

author = "Jaume Llibre and Claudia Valls",

year = "2018",

month = aug,

day = "1",

doi = "10.3934/dcdsb.2018070",

language = "English",

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pages = "2475--2485",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

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T1 - Algebraic limit cycles for quadratic polynomial differential systems

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2018/8/1

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N2 - © 2018 American Institute of Mathematical Sciences. All Rights Reserved. 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.

AB - © 2018 American Institute of Mathematical Sciences. All Rights Reserved. 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.

U2 - 10.3934/dcdsb.2018070

DO - 10.3934/dcdsb.2018070

M3 - Article

VL - 23

SP - 2475

EP - 2485

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 6

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