Lower bounds for the number of limit cycles of trigonometric Abel equations

A. Gasull; M. J. Álvarez; J. Yu

doi:10.1016/j.jmaa.2007.12.016

Lower bounds for the number of limit cycles of trigonometric Abel equations

A. Gasull, M. J. Álvarez, J. Yu

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

16 Citas (Scopus)

Resumen

We consider the Abel equation over(x, ̇) = A (t) x3 + B (t) x2, where A (t) and B (t) are trigonometric polynomials of degree n and m, respectively, and we give lower bounds for its number of isolated periodic orbits for some values of n and m. These lower bounds are obtained by two different methods: the study of the perturbations of some Abel equations having a continuum of periodic orbits and the Hopf-type bifurcation of periodic orbits from the solution x = 0. © 2007 Elsevier Inc. All rights reserved.

Idioma original	Inglés
Páginas (desde-hasta)	682-693
Publicación	Journal of Mathematical Analysis and Applications
Volumen	342
N.º	1
DOI	https://doi.org/10.1016/j.jmaa.2007.12.016
Estado	Publicada - 1 jun 2008

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title = "Lower bounds for the number of limit cycles of trigonometric Abel equations",

abstract = "We consider the Abel equation over(x,{\. }) = A (t) x3 + B (t) x2, where A (t) and B (t) are trigonometric polynomials of degree n and m, respectively, and we give lower bounds for its number of isolated periodic orbits for some values of n and m. These lower bounds are obtained by two different methods: the study of the perturbations of some Abel equations having a continuum of periodic orbits and the Hopf-type bifurcation of periodic orbits from the solution x = 0. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

keywords = "Abel equation, Melnikov functions, Periodic orbit",

author = "A. Gasull and {\'A}lvarez, {M. J.} and J. Yu",

year = "2008",

month = jun,

day = "1",

doi = "10.1016/j.jmaa.2007.12.016",

language = "English",

volume = "342",

pages = "682--693",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Lower bounds for the number of limit cycles of trigonometric Abel equations

AU - Gasull, A.

AU - Álvarez, M. J.

AU - Yu, J.

PY - 2008/6/1

Y1 - 2008/6/1

N2 - We consider the Abel equation over(x, ̇) = A (t) x3 + B (t) x2, where A (t) and B (t) are trigonometric polynomials of degree n and m, respectively, and we give lower bounds for its number of isolated periodic orbits for some values of n and m. These lower bounds are obtained by two different methods: the study of the perturbations of some Abel equations having a continuum of periodic orbits and the Hopf-type bifurcation of periodic orbits from the solution x = 0. © 2007 Elsevier Inc. All rights reserved.

AB - We consider the Abel equation over(x, ̇) = A (t) x3 + B (t) x2, where A (t) and B (t) are trigonometric polynomials of degree n and m, respectively, and we give lower bounds for its number of isolated periodic orbits for some values of n and m. These lower bounds are obtained by two different methods: the study of the perturbations of some Abel equations having a continuum of periodic orbits and the Hopf-type bifurcation of periodic orbits from the solution x = 0. © 2007 Elsevier Inc. All rights reserved.

KW - Abel equation

KW - Melnikov functions

KW - Periodic orbit

U2 - 10.1016/j.jmaa.2007.12.016

DO - 10.1016/j.jmaa.2007.12.016

M3 - Article

SN - 0022-247X

VL - 342

SP - 682

EP - 693

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Lower bounds for the number of limit cycles of trigonometric Abel equations

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