On the homoclinic orbits in a class of two-degree-of-freedom systems under the resonance conditions. (English) Zbl 1007.70018
Summary: We investigate a class of two-degree-of-freedom systems in resonance under external parametric excitation. The existence of periodic solutions is proved by the method of multiple scales. This systems can be transformed into Wiggins systems under some conditions. Finally, we give analytical conditions for the existence of homoclinic orbits.
MSC:
| 70K44 | Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics |
| 70K30 | Nonlinear resonances for nonlinear problems in mechanics |
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
