Subharmonic bouncing solutions for a class of sublinear impact oscillators with indefinite weight. (English) Zbl 1541.34058
The motion of a particle attached to a nonlinear spring and bouncing elastically against a fixed barrier can be modelled by a set of equations of forced sublinear impact oscillators of Hill’s type with indefinite weight. In this paper, the authors investigate the existence and multiplicity of subharmonic bouncing solutions in a class of such systems. By applying a series of coordinate transformations, they first obtain a nearly integrable Hamiltonian. Then, they show that the Poincaré map of the new system is a “twist” map. Finally, they prove the existence of infinite numbers of subharmonic bouncing solutions by using the Poincaré-Birkhoff twist theorem.
Reviewer: Kwok-wai Chung (Hong Kong)
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 37E40 | Dynamical aspects of twist maps |
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