Symmetry and bifurcations of planar configurations of the N-body and other problems

Kathryn Glass

doi:10.1080/713603736

Symmetry and bifurcations of planar configurations of the N-body and other problems

Kathryn Glass^*

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

We describe a system of equations containing a real parameter β and an integer parameter N ≥ 2. Equilibria of these equations are in turn asymptotic shapes of systems of repelling particles for β = 0, central configurations with equal mass of the N-body problem for β = 1, and approximate solutions of a sphere-packing problem for β large. We introduce some asymmetric equilibria of these equations for N = 6 and 7, and identify and discuss the bifurcations that occur in this system for 5 ≤ N ≤ 8.

Original language	English
Pages (from-to)	59-73
Number of pages	15
Journal	Dynamical Systems
Volume	15
Issue number	2
DOIs	https://doi.org/10.1080/713603736
Publication status	Published - 2000
Externally published	Yes

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10.1080/713603736

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abstract = "We describe a system of equations containing a real parameter β and an integer parameter N ≥ 2. Equilibria of these equations are in turn asymptotic shapes of systems of repelling particles for β = 0, central configurations with equal mass of the N-body problem for β = 1, and approximate solutions of a sphere-packing problem for β large. We introduce some asymmetric equilibria of these equations for N = 6 and 7, and identify and discuss the bifurcations that occur in this system for 5 ≤ N ≤ 8.",

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N2 - We describe a system of equations containing a real parameter β and an integer parameter N ≥ 2. Equilibria of these equations are in turn asymptotic shapes of systems of repelling particles for β = 0, central configurations with equal mass of the N-body problem for β = 1, and approximate solutions of a sphere-packing problem for β large. We introduce some asymmetric equilibria of these equations for N = 6 and 7, and identify and discuss the bifurcations that occur in this system for 5 ≤ N ≤ 8.

AB - We describe a system of equations containing a real parameter β and an integer parameter N ≥ 2. Equilibria of these equations are in turn asymptotic shapes of systems of repelling particles for β = 0, central configurations with equal mass of the N-body problem for β = 1, and approximate solutions of a sphere-packing problem for β large. We introduce some asymmetric equilibria of these equations for N = 6 and 7, and identify and discuss the bifurcations that occur in this system for 5 ≤ N ≤ 8.

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U2 - 10.1080/713603736

DO - 10.1080/713603736

M3 - Article

AN - SCOPUS:0346108449

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VL - 15

SP - 59

EP - 73

JO - Dynamical Systems

JF - Dynamical Systems

IS - 2

ER -

Symmetry and bifurcations of planar configurations of the N-body and other problems

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