An upper bound of the index of an equilibrium point in the plane

Jaume Llibre; José Martínez-Alfaro

doi:https://doi.org/10.1016/j.jde.2012.07.001

An upper bound of the index of an equilibrium point in the plane

Jaume Llibre, José Martínez-Alfaro

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index. © 2012 Elsevier Inc.

Original language	English
Pages (from-to)	2460-2473
Journal	Journal of Differential Equations
Volume	253
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2012.07.001
Publication status	Published - 15 Oct 2012

Keywords

Gradient systems
Hamiltonian systems
Index
Planar differential systems

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N2 - We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index. © 2012 Elsevier Inc.

AB - We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index. © 2012 Elsevier Inc.

KW - Gradient systems

KW - Hamiltonian systems

KW - Index

KW - Planar differential systems

UR - https://ddd.uab.cat/record/150494

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M3 - Article

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SP - 2460

EP - 2473

IS - 8

ER -

An upper bound of the index of an equilibrium point in the plane

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Keywords

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