Generic finiteness for a class of symmetric planar central configurations of the six-body problem and the six-vortex problem

DOI10.1007/s10884-019-09765-yzbMath1480.70017arXiv1811.08681OpenAlexW2901972123WikidataQ127809813 ScholiaQ127809813MaRDI QIDQ2211279

Bo-Yu Pan, Thiago Dias

Publication date: 11 November 2020

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08681

zbMATH Keywords

elimination theoryGroebner basis\(n\)-body problemcentral configurationJacobian criterionn-vortex problem

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) (n)-body problems (70F10)

Related Items (2)

Exploring circulations yielding no vortex equilibria ⋮ Toward finiteness of central configurations for the planar six-body problem by symbolic computations. I: Determine diagrams and orders

Uses Software

• SageMath
• SINGULAR
• GitHub
• VortexCalculations

Cites Work

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• Relative equilibria in the four-vortex problem with two pairs of equal vorticities
• Twisted angles for central configurations formed by two twisted regular polygons
• Finiteness of central configurations of five bodies in the plane
• Symmetric planar central configurations of five bodies: Euler plus two
• Existence of symmetric central configurations
• Elementary structure of real algebraic varieties
• Finiteness of relative equilibria of the four-body problem
• Rosette central configurations, degenerate central configurations and bifurcations
• Symmetric central configurations of the spatial n-body problem
• Finiteness and bifurcations of some symmetrical classes of central configurations
• Mathematical problems for the next century
• Planar symmetric concave central configurations in Newtonian four-body problems
• Numbers of relative equilibria in the planar four-vortex problem: some special cases
• Generic Finiteness for Dziobek Configurations
• Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities
• New equations for central configurations and generic finiteness
• Relative equilibria of the four-body problem
• Symmetry of planar four-body convex central configurations
• Finiteness of stationary configurations of the four-vortex problem
• Stationary Configurations of Point Vortices

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