The Existence of Aubry–Mather sets for the Fermi–Ulam Model

Zhenbang Cao, Celso Grebogi, Denghui Li* (Corresponding Author), Jianhua Xie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Fermi–Ulam model, which can be described as a particle moving freely between two vertical rigid walls; the left one being fixed, whereas the right one moves according to a regular periodic function. The particle is elastically reflected when hitting the walls. We show that the dynamics of the model can be described by an area-preserving monotone twist map. Thus, the Aubry–Mather sets exist for every rotation number in the rotation interval. Consequently, this gives a description of global dynamics behavior, particularly a large class of periodic and quasiperiodic orbits for the model.
Original languageEnglish
Article number12
Number of pages12
JournalQualitative Theory of Dynamical Systems
Volume20
Early online date21 Jan 2021
DOIs
Publication statusPublished - 21 Jan 2021

Keywords

  • Fermi-Ulam model
  • Aubry-Mather set
  • Twist map

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