On the global dynamical properties of a Fermi–Ulam model

Zhenbang Cao; Denghui Li; Celso Grebogi; Yuan Yue; Jianhua Xie

doi:10.1080/10236198.2021.2003793

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 journal › Article › peer-review

2 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1647-1656
Number of pages	10
Journal	Journal of Difference Equations and Applications
Volume	27
Issue number	12
Early online date	17 Nov 2021
DOIs	https://doi.org/10.1080/10236198.2021.2003793
Publication status	Published - 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.

Keywords

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

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10.1080/10236198.2021.2003793Licence: Unspecified

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title = "On the global dynamical properties of a Fermi–Ulam model",

abstract = "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.",

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T1 - On the global dynamical properties of a Fermi–Ulam model

AU - Cao, Zhenbang

AU - Li, Denghui

AU - Grebogi, Celso

AU - Yue, Yuan

AU - Xie, Jianhua

N1 - 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.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - 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.

AB - 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.

KW - Aubry–Mather set

KW - Fermi–Ulam model

KW - non-smooth dynamical system

KW - twist map

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SP - 1647

EP - 1656

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 12

ER -

On the global dynamical properties of a Fermi–Ulam model

Abstract

Bibliographical note

Keywords

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