On the global dynamical properties of a Fermi–Ulam model

Zhenbang Cao, Denghui Li*, Celso Grebogi, Yuan Yue, Jianhua Xie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We consider a Fermi–Ulam model describing a particle which moves freely between two parallel walls and is reflected elastically when hitting the walls. The walls are supposed to oscillate according to a given regular periodic function. We show that in high energy situation, the global dynamics of this model can be described by an exact area-preserving monotone twist map. Then the existence of abundant periodic orbits and quasi-periodic orbits is proved based on the Aubry–Mather theory.

Original languageEnglish
Pages (from-to)1647-1656
Number of pages10
JournalJournal of Difference Equations and Applications
Issue number12
Early online date17 Nov 2021
Publication statusPublished - 1 Dec 2021

Bibliographical note

Funding Information:
This work is supported by the National Natural Science Foundations of China (12172306 and 11732014). The authors express their gratitude to the reviewers for fruitful comments and suggestions.


  • Aubry–Mather set
  • Fermi–Ulam model
  • non-smooth dynamical system
  • twist map


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