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<p>This paper considers the dynamics of an oscillator bouncing off a quasi-periodically moving wall. It is shown that the resonance of elasticity constant and quasi-periodic frequencies of the motion of wall plays an important role in the dynamics of oscillator. Moreover, it is obtained that the oscillator is stable in three different cases: Strong Non-resonance, Non-resonance and Resonance. This result depends on several degenerate KAM theorems recently developed.</p>

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Stability of an Impact Oscillator with a Quasi-Periodically Moving Wall

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Zhichao Ma

摘要

This paper considers the dynamics of an oscillator bouncing off a quasi-periodically moving wall. It is shown that the resonance of elasticity constant and quasi-periodic frequencies of the motion of wall plays an important role in the dynamics of oscillator. Moreover, it is obtained that the oscillator is stable in three different cases: Strong Non-resonance, Non-resonance and Resonance. This result depends on several degenerate KAM theorems recently developed.