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

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	E-pub ahead of print - 17 Feb 2023

Keywords

Bouncing ball
Invariant curve
Quasiperiodic motion
Boundedness

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

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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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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 - 2023/2/17

Y1 - 2023/2/17

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

VL - 169

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

M1 - 113268

ER -

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

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