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

作者：Llibre Jaume; Martinez Alfaro Jose^*

来源：Journal of Differential Equations, 2012, 253(8): 2460-2473.

DOI：10.1016/j.jde.2012.07.001

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

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 Pi where the gradient and Hamiltonian components are linearly dependent. The number of branches of Pi starting at the equilibrium point determines the upper bound of the index.

• 出版日期2012-10-15