Limit sets within curves where trajectories converge to

作者：Ramazi Pouria^*; Jardon Kojakhmetov Hildeberto; Cao Ming

来源：Applied Mathematics Letters, 2017, 68: 94-100.

DOI：10.1016/j.aml.2017.01.005

• Limit set
• Convergence
• Curve
• Poincare-Bendixson theorem

For continuously differentiable vector fields, we characterize the omega limit set of a trajectory converging to a compact curve Gamma subset of R-n. In particular, the limit set is either a fixed point or a continuum of fixed points if Gamma is a simple open curve; otherwise, the limit set can in addition be either a closed orbit or a number of fixed points with compatibly oriented orbits connecting them. An implication of the result is a tightened-up version of the Poincare-Bendixson theorem.

• 出版日期2017-6