The Co-circular Central Configurations of the 5-Body Problem

Jaume Llibre; Claudia Valls

doi:https://doi.org/10.1007/s10884-015-9429-y

The Co-circular Central Configurations of the 5-Body Problem

Jaume Llibre, Claudia Valls

Department of Mathematics

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

4 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media New York. Chenciner in 2001 asked: Is the regular n-gon with equal masses the unique central configuration such that all the bodies lie on a circle, and the center of mass coincides with the center of the circle? This question has a positive answer for n=3. Hampton in 2003 proved that also this question has a positive answer for n=4. Here we provide a positive answer for n=5.

Original language	English
Pages (from-to)	55-67
Journal	Journal of Dynamics and Differential Equations
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s10884-015-9429-y
Publication status	Published - 1 Jan 2015

Keywords

5-body problem
Central configuration
Co-circular central configuration
Regular n-gon

Access to Document

https://doi.org/10.1007/s10884-015-9429-y

https://ddd.uab.cat/record/145295

Cite this

@article{a07f400a94b342ec9853258ac42a41b6,

title = "The Co-circular Central Configurations of the 5-Body Problem",

abstract = "{\textcopyright} 2015, Springer Science+Business Media New York. Chenciner in 2001 asked: Is the regular n-gon with equal masses the unique central configuration such that all the bodies lie on a circle, and the center of mass coincides with the center of the circle? This question has a positive answer for n=3. Hampton in 2003 proved that also this question has a positive answer for n=4. Here we provide a positive answer for n=5.",

keywords = "5-body problem, Central configuration, Co-circular central configuration, Regular n-gon",

author = "Jaume Llibre and Claudia Valls",

year = "2015",

month = jan,

day = "1",

doi = "https://doi.org/10.1007/s10884-015-9429-y",

language = "English",

volume = "27",

pages = "55--67",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - The Co-circular Central Configurations of the 5-Body Problem

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2015/1/1

Y1 - 2015/1/1

N2 - © 2015, Springer Science+Business Media New York. Chenciner in 2001 asked: Is the regular n-gon with equal masses the unique central configuration such that all the bodies lie on a circle, and the center of mass coincides with the center of the circle? This question has a positive answer for n=3. Hampton in 2003 proved that also this question has a positive answer for n=4. Here we provide a positive answer for n=5.

AB - © 2015, Springer Science+Business Media New York. Chenciner in 2001 asked: Is the regular n-gon with equal masses the unique central configuration such that all the bodies lie on a circle, and the center of mass coincides with the center of the circle? This question has a positive answer for n=3. Hampton in 2003 proved that also this question has a positive answer for n=4. Here we provide a positive answer for n=5.

KW - 5-body problem

KW - Central configuration

KW - Co-circular central configuration

KW - Regular n-gon

U2 - https://doi.org/10.1007/s10884-015-9429-y

DO - https://doi.org/10.1007/s10884-015-9429-y

M3 - Article

VL - 27

SP - 55

EP - 67

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 1

ER -

The Co-circular Central Configurations of the 5-Body Problem

Abstract

Keywords

Access to Document

Fingerprint

Cite this