Periodic and Quasiperiodic Solutions of a Forced Discontinuous Oscillator

• Denghui Li ^[3] ; Xiaoming Zhang ^[1] ; Biliu Zhou ^[2]
  1. [1] Nanjing University of Aeronautics and Astronautics

     Nanjing University of Aeronautics and Astronautics

     China

     
  2. [2] Changshu Institute of Technology

     Changshu Institute of Technology

     China

     
  3. [3] Hexi University & Changshu Institute of Technology

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
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• Resumen

  • 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.