Cyclicity versus center problem

Armengol Gasull; Jaume Giné

doi:10.1007/s12346-010-0022-9

Cyclicity versus center problem

Armengol Gasull, Jaume Giné

Departament de Matemàtiques

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Resum

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed. © Springer Basel AG 2010.

Idioma original	Anglès
Pàgines (de-a)	101-113
Revista	Qualitative Theory of Dynamical Systems
Volum	9
Número	1-2
DOIs	https://doi.org/10.1007/s12346-010-0022-9
Estat de la publicació	Publicada - 1 de gen. 2010

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10.1007/s12346-010-0022-9

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@article{91827648bdaa4823baa0f4766177f10c,

title = "Cyclicity versus center problem",

abstract = "We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed. {\textcopyright} Springer Basel AG 2010.",

keywords = "Cyclicity, Focal quantities, Limit cycles, Lyapunov constants, Polynomial differential system",

author = "Armengol Gasull and Jaume Gin{\'e}",

year = "2010",

month = jan,

day = "1",

doi = "10.1007/s12346-010-0022-9",

language = "English",

volume = "9",

pages = "101--113",

journal = "Qualitative Theory of Dynamical Systems",

issn = "1575-5460",

publisher = "Springer Science + Business Media",

number = "1-2",

}

TY - JOUR

T1 - Cyclicity versus center problem

AU - Gasull, Armengol

AU - Giné, Jaume

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed. © Springer Basel AG 2010.

AB - We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed. © Springer Basel AG 2010.

KW - Cyclicity

KW - Focal quantities

KW - Limit cycles

KW - Lyapunov constants

KW - Polynomial differential system

U2 - 10.1007/s12346-010-0022-9

DO - 10.1007/s12346-010-0022-9

M3 - Article

SN - 1575-5460

VL - 9

SP - 101

EP - 113

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

IS - 1-2

ER -

Cyclicity versus center problem

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