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

Jaume Llibre, José Martínez-Alfaro

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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 languageEnglish
Pages (from-to)2460-2473
JournalJournal of Differential Equations
Volume253
Issue number8
DOIs
Publication statusPublished - 15 Oct 2012

Keywords

  • Gradient systems
  • Hamiltonian systems
  • Index
  • Planar differential systems

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    Llibre, J., & Martínez-Alfaro, J. (2012). An upper bound of the index of an equilibrium point in the plane. Journal of Differential Equations, 253(8), 2460-2473. https://doi.org/10.1016/j.jde.2012.07.001