Generic finiteness for Dziobek configurations

Richard Moeckel

doi:10.1090/s0002-9947-01-02828-8

Generic finiteness for Dziobek configurations

Richard Moeckel

School of Mathematics

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

37 Scopus citations

Abstract

The goal of this paper is to show that for almost all choices of n masses, mi, there are only finitely many central configurations of the Newtonian ?i-body problem for which the bodies span a space of dimension n -2 (such a central configuration is called a Dziobek configuration). The result applies in particular to two-dimensional configurations of four bodies and threedimensional configurations of five bodies.

Original language	English (US)
Pages (from-to)	4673-4686
Number of pages	14
Journal	Transactions of the American Mathematical Society
Volume	353
Issue number	11
DOIs	https://doi.org/10.1090/s0002-9947-01-02828-8
State	Published - 2001

Keywords

Celestial mechanics
Central configurations
N-body problem

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10.1090/s0002-9947-01-02828-8

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abstract = "The goal of this paper is to show that for almost all choices of n masses, mi, there are only finitely many central configurations of the Newtonian ?i-body problem for which the bodies span a space of dimension n -2 (such a central configuration is called a Dziobek configuration). The result applies in particular to two-dimensional configurations of four bodies and threedimensional configurations of five bodies.",

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AB - The goal of this paper is to show that for almost all choices of n masses, mi, there are only finitely many central configurations of the Newtonian ?i-body problem for which the bodies span a space of dimension n -2 (such a central configuration is called a Dziobek configuration). The result applies in particular to two-dimensional configurations of four bodies and threedimensional configurations of five bodies.

KW - Celestial mechanics

KW - Central configurations

KW - N-body problem

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

ER -

Generic finiteness for Dziobek configurations

Abstract

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