Stability of certain planar unbounded polycycles

Armengol Gasull; Víctor Mañosa; Francesc Mañosas

doi:10.1016/S0022-247X(02)00027-6

Stability of certain planar unbounded polycycles

Armengol Gasull, Víctor Mañosa, Francesc Mañosas

Departament de Matemàtiques

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Resum

We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.

Idioma original	Anglès
Pàgines (de-a)	332-351
Revista	Journal of Mathematical Analysis and Applications
Volum	269
Número	1
DOIs	https://doi.org/10.1016/S0022-247X(02)00027-6
Estat de la publicació	Publicada - 1 de maig 2002

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10.1016/S0022-247X(02)00027-6

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https://www.scopus.com/pages/publications/0036576560

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title = "Stability of certain planar unbounded polycycles",

abstract = "We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. {\textcopyright} 2002 Elsevier Science (USA). All rights reserved.",

keywords = "Bifurcation of limit cycles, Polycycle, Polynomial vector field, Stability",

author = "Armengol Gasull and V{\'i}ctor Ma{\~n}osa and Francesc Ma{\~n}osas",

year = "2002",

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doi = "10.1016/S0022-247X(02)00027-6",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Stability of certain planar unbounded polycycles

AU - Gasull, Armengol

AU - Mañosa, Víctor

AU - Mañosas, Francesc

PY - 2002/5/1

Y1 - 2002/5/1

N2 - We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.

AB - We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle. © 2002 Elsevier Science (USA). All rights reserved.

KW - Bifurcation of limit cycles

KW - Polycycle

KW - Polynomial vector field

KW - Stability

UR - https://www.scopus.com/pages/publications/0036576560

U2 - 10.1016/S0022-247X(02)00027-6

DO - 10.1016/S0022-247X(02)00027-6

M3 - Article

SN - 0022-247X

VL - 269

SP - 332

EP - 351

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Stability of certain planar unbounded polycycles

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