论文标题
强制非线性振荡器的不整合性
Nonintegrability of Forced Nonlinear Oscillators
论文作者
论文摘要
作者最近的论文（S.提供了具有单度自由汉密尔顿系统的时间周期性扰动形式的强制非线性振荡器。在这里，采用了Bogoyavlenskij意义上的非整合性的概念，并且还需要第一个积分和交换矢量字段才能实现或复杂的词法对小参数依赖。在本文中，我们回顾了理论，并继续证明它们的实用性。特别是，我们考虑了定期强迫抑制的摆，并证明了其在上述含义中的不整合性。
In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to integrability of nearly integrable dynamical systems near regular level sets, submitted for publication, and K.~Yagasaki, Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits, submitted for publication), two different techniques which allow us to prove the real-analytic or complex-meromorphic nonintegrability of forced nonlinear oscillators having the form of time-periodic perturbations of single-degree-of-freedom Hamiltonian systems were provided. Here the concept of nonintegrability in the Bogoyavlenskij sense is adopted and the first integrals and commutative vector fields are also required to depend real-analytically or complex-meromorphically on the small parameter. In this paper we review the theories and continue to demonstrate their usefulness. In particular, we consider the periodically forced damped pendulum and prove its nonintegrability in the above meaning.
