Boundedness of solutions for a bouncing ball model with quasiperiodic moving wall

Denghui Li; Xiaoming Zhang; Xianbin Liu; Jianhua Xie; Celso Grebogi

doi:10.1016/j.chaos.2023.113268

Boundedness of solutions for a bouncing ball model with quasiperiodic moving wall

Denghui Li, Xiaoming Zhang^* (Corresponding Author), Xianbin Liu, Jianhua Xie, Celso Grebogi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this work, we consider the model of a free falling ball on a wall that is elastically reflected. The wall is supposed to move in the vertical direction according to a given quasiperiodic function. Based on the invariant curve theorem of smooth quasiperiodic twist map, we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the system.

Original language	English
Article number	113268
Journal	Chaos, Solitons & Fractals
Volume	169
Early online date	17 Feb 2023
DOIs	https://doi.org/10.1016/j.chaos.2023.113268
Publication status	Published - Apr 2023

Bibliographical note

Acknowledgments
This work is supported by the National Natural Science Foundation of China (No. 12172306, 12172167).

Data Availability Statement

No data was used for the research described in the article.

Keywords

Bouncing ball
Invariant curve
Quasiperiodic motion
Boundedness

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10.1016/j.chaos.2023.113268

Li_etal_CSF_Boundedness_of_Solutions_AAMAccepted author manuscript, 166 KBLicence: CC BY-NC-ND

https://www.sciencedirect.com/science/article/pii/S0960077923001698

Cite this

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title = "Boundedness of solutions for a bouncing ball model with quasiperiodic moving wall",

abstract = "In this work, we consider the model of a free falling ball on a wall that is elastically reflected. The wall is supposed to move in the vertical direction according to a given quasiperiodic function. Based on the invariant curve theorem of smooth quasiperiodic twist map, we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the system.",

keywords = "Bouncing ball, Invariant curve, Quasiperiodic motion, Boundedness",

author = "Denghui Li and Xiaoming Zhang and Xianbin Liu and Jianhua Xie and Celso Grebogi",

note = "Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 12172306, 12172167).",

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language = "English",

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TY - JOUR

T1 - Boundedness of solutions for a bouncing ball model with quasiperiodic moving wall

AU - Li, Denghui

AU - Zhang, Xiaoming

AU - Liu, Xianbin

AU - Xie, Jianhua

AU - Grebogi, Celso

N1 - Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 12172306, 12172167).

PY - 2023/4

Y1 - 2023/4

N2 - In this work, we consider the model of a free falling ball on a wall that is elastically reflected. The wall is supposed to move in the vertical direction according to a given quasiperiodic function. Based on the invariant curve theorem of smooth quasiperiodic twist map, we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the system.

AB - In this work, we consider the model of a free falling ball on a wall that is elastically reflected. The wall is supposed to move in the vertical direction according to a given quasiperiodic function. Based on the invariant curve theorem of smooth quasiperiodic twist map, we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the system.

KW - Bouncing ball

KW - Invariant curve

KW - Quasiperiodic motion

KW - Boundedness

U2 - 10.1016/j.chaos.2023.113268

DO - 10.1016/j.chaos.2023.113268

M3 - Article

SN - 0960-0779

VL - 169

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

M1 - 113268

ER -

Boundedness of solutions for a bouncing ball model with quasiperiodic moving wall

Abstract

Bibliographical note

Data Availability Statement

Keywords

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