Periodic and Quasiperiodic Solutions of a Forced Discontinuous Oscillator

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-08-19 DOI:10.1007/s12346-024-01094-w

Denghui Li, Xiaoming Zhang, Biliu Zhou

引用次数: 0

Abstract

In this paper we consider a forced oscillator with a discontinuous restoring force. By the Aubry–Mather theory we prove that there exist infinitely many periodic and quasiperiodic solutions. The proof relies on analysing the generating function of the system. The approach is applicable to studying the dynamics of more general forced nonsmooth oscillators of Hamiltonian type.

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强迫非连续振荡器的周期和准周期解法

在本文中，我们考虑了一个具有不连续恢复力的受迫振荡器。通过奥布里-马瑟理论，我们证明存在无限多的周期和准周期解。该证明依赖于对系统生成函数的分析。这种方法适用于研究更一般的哈密顿型受迫非光滑振荡器的动力学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.