Alien limit cycles in Lienard equations

作者：Coll B; Dumortier F; Prohens R^*

来源：Journal of Differential Equations, 2013, 254(3): 1582-1600.

DOI：10.1016/j.jde.2012.11.005

• Planar vector field
• Lienard equation
• Hamiltonian perturbation
• Limit cycle
• Abelian integral
• 2-Saddle cycle

This paper aims at providing an example of a family of polynomial Lienard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. The Hamiltonian represents a truncated pendulum of degree 4. In comparison to a former polynomial example, not only the equations are simpler but a lot of tedious calculations can be avoided, making the example also interesting with respect to simplicity in treatment.

• 出版日期2013-2-1