拟周期强迫Morse振子的长范围混沌

Long Range Chaotic Behavior of Quasiperiodically Forced Morse Oscillator

该文定性研究了拟周期强迫Morse振子的动力学性质,该模型是描述分子在外部拟周期电磁作用下分裂的一个经典模型.通过引进著名的McGeHee变换,并应用拟周期扰动的广义Melnikov方法,证明了该系统存在Smale马蹄意义下的混沌.所得的结果为以前的数值结果提供了一个解析证实.

In this paper, qualitative dynamics of a quasiperiodically forced oscillator is studied as a (classical) model for molecular dissociation under external quasipeiodic electromagnetic force. By introducing the famous McGehee transformation and applying the generalized homoclinic Melnikov method, it is rigorously shown that this model has chaotic dynamics in the sense of Smale horseshoes. The (results) provide an analytic verification of the previous numerical results.