Rational limit cycles of abel equations

Jaume Llibre; Claudia Valls

doi:10.3934/CPAA.2021007

Rational limit cycles of abel equations

Jaume Llibre^*, Claudia Valls

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

University of Lisbon (ULisboa)

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

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Resum

We deal with Abel equations dy=dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most two rational limit cycles and we characterize when this happens. Moreover we provide examples of these Abel equations with two nontrivial rational limit cycles.

Idioma original	Anglès
Pàgines (de-a)	1077-1089
Nombre de pàgines	13
Revista	Communications on Pure and Applied Analysis
Volum	20
Número	3
DOIs	https://doi.org/10.3934/CPAA.2021007
Estat de la publicació	Publicada - de març 2021

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10.3934/CPAA.2021007

https://ddd.uab.cat/record/239782

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@article{03c63319349246b7841bd44079394170,

title = "Rational limit cycles of abel equations",

abstract = "We deal with Abel equations dy=dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most two rational limit cycles and we characterize when this happens. Moreover we provide examples of these Abel equations with two nontrivial rational limit cycles.",

keywords = "Abel equations, Algebraic limit cycles, Rational limit cycles",

author = "Jaume Llibre and Claudia Valls",

year = "2021",

month = mar,

doi = "10.3934/CPAA.2021007",

language = "English",

volume = "20",

pages = "1077--1089",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - Rational limit cycles of abel equations

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2021/3

Y1 - 2021/3

N2 - We deal with Abel equations dy=dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most two rational limit cycles and we characterize when this happens. Moreover we provide examples of these Abel equations with two nontrivial rational limit cycles.

AB - We deal with Abel equations dy=dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most two rational limit cycles and we characterize when this happens. Moreover we provide examples of these Abel equations with two nontrivial rational limit cycles.

KW - Abel equations

KW - Algebraic limit cycles

KW - Rational limit cycles

UR - https://www.scopus.com/pages/publications/85103752974

U2 - 10.3934/CPAA.2021007

DO - 10.3934/CPAA.2021007

M3 - Article

AN - SCOPUS:85103752974

SN - 1534-0392

VL - 20

SP - 1077

EP - 1089

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 3

ER -

Rational limit cycles of abel equations

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