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 language | English |
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Article number | 12 |
Number of pages | 12 |
Journal | Qualitative Theory of Dynamical Systems |
Volume | 20 |
Early online date | 21 Jan 2021 |
DOIs | |
Publication status | Published - 21 Jan 2021 |
Bibliographical note
AcknowledgementsThis work is supported by the National Natural Science Foundations of China (11732014). The authors express their gratitude to the reviewer for fruitful comments and suggestions.
Keywords
- Fermi-Ulam model
- Aubry-Mather set
- Twist map