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

Departament de Matemàtiques

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Resum

© 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.

Idioma original	Anglès
Pàgines (de-a)	2475-2485
Revista	Discrete and Continuous Dynamical Systems - Series B
Volum	23
Número	6
DOIs	https://doi.org/10.3934/dcdsb.2018070
Estat de la publicació	Publicada - 1 d’ag. 2018

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10.3934/dcdsb.2018070

https://ddd.uab.cat/record/199341

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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",

volume = "23",

pages = "2475--2485",

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

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "6",

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TY - JOUR

T1 - Algebraic limit cycles for quadratic polynomial differential systems

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2018/8/1

Y1 - 2018/8/1

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

SN - 1531-3492

VL - 23

SP - 2475

EP - 2485

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 6

ER -

Algebraic limit cycles for quadratic polynomial differential systems

Resum

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