The focus-centre problem for a type of degenerate system

Armengol Gasull; Jaume Llibre; Víctor Mañosa; Francesc Mañosas

doi:10.1088/0951-7715/13/3/311

The focus-centre problem for a type of degenerate system

Armengol Gasull, Jaume Llibre, Víctor Mañosa, Francesc Mañosas

Departament de Matemàtiques

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Resum

We consider differential systems in the plane defined by the sum of two homogeneous vector fields. We assume that the origin is a degenerate singular point for these differential systems. We characterize when the singular point is of focus-centre type in a generic case. The problem of its local stability is also considered. We compute the first generalized Lyapunov constant when some non-degeneracy conditions are assumed.

Idioma original	Anglès
Pàgines (de-a)	699-729
Revista	Nonlinearity
Volum	13
DOIs	https://doi.org/10.1088/0951-7715/13/3/311
Estat de la publicació	Publicada - 1 de maig 2000

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10.1088/0951-7715/13/3/311

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title = "The focus-centre problem for a type of degenerate system",

abstract = "We consider differential systems in the plane defined by the sum of two homogeneous vector fields. We assume that the origin is a degenerate singular point for these differential systems. We characterize when the singular point is of focus-centre type in a generic case. The problem of its local stability is also considered. We compute the first generalized Lyapunov constant when some non-degeneracy conditions are assumed.",

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

year = "2000",

month = may,

day = "1",

doi = "10.1088/0951-7715/13/3/311",

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journal = "Nonlinearity",

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T1 - The focus-centre problem for a type of degenerate system

AU - Gasull, Armengol

AU - Llibre, Jaume

AU - Mañosa, Víctor

AU - Mañosas, Francesc

PY - 2000/5/1

Y1 - 2000/5/1

N2 - We consider differential systems in the plane defined by the sum of two homogeneous vector fields. We assume that the origin is a degenerate singular point for these differential systems. We characterize when the singular point is of focus-centre type in a generic case. The problem of its local stability is also considered. We compute the first generalized Lyapunov constant when some non-degeneracy conditions are assumed.

AB - We consider differential systems in the plane defined by the sum of two homogeneous vector fields. We assume that the origin is a degenerate singular point for these differential systems. We characterize when the singular point is of focus-centre type in a generic case. The problem of its local stability is also considered. We compute the first generalized Lyapunov constant when some non-degeneracy conditions are assumed.

U2 - 10.1088/0951-7715/13/3/311

DO - 10.1088/0951-7715/13/3/311

M3 - Article

SN - 0951-7715

VL - 13

SP - 699

EP - 729

JO - Nonlinearity

JF - Nonlinearity

ER -

The focus-centre problem for a type of degenerate system

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