The focus-centre problem for a type of degenerate system

Armengol Gasull; Jaume Llibre; Víctor Mañosa; Francesc Mañosas

doi:https://doi.org/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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

39 Citations (Scopus)

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.

Original language	English
Pages (from-to)	699-729
Journal	Nonlinearity
Volume	13
DOIs	https://doi.org/10.1088/0951-7715/13/3/311
Publication status	Published - 1 May 2000

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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.",

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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 - https://doi.org/10.1088/0951-7715/13/3/311

DO - https://doi.org/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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