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.
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Acknowledgements
This 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.
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Cao, Z., Grebogi, C., Li, D. et al. The Existence of Aubry–Mather sets for the Fermi–Ulam Model. Qual. Theory Dyn. Syst. 20, 12 (2021). https://doi.org/10.1007/s12346-021-00446-0
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DOI: https://doi.org/10.1007/s12346-021-00446-0