Planar \(N\)-body central configurations with a homogeneous potential (Q2005616)

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English	Planar \(N\)-body central configurations with a homogeneous potential	scientific article

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scholarly article

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Planar \(N\)-body central configurations with a homogeneous potential (English)

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zbMATH Open document ID

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10.1007/s10569-019-9898-0

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Marshall Hampton

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Celestial Mechanics and Dynamical Astronomy

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publication date

8 October 2020

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full work available at URL

https://arxiv.org/abs/1810.13011

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Mathematics Subject Classification ID

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zbMATH DE Number

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describes a project that uses

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VortexCalculations

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MaRDI profile type

MaRDI publication profile

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Integral manifolds of the \(N\)-body problem

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On a paper of Moeckel on central configurations

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Open problem 1: Are Palmore's ``ignored estimates'' on the number of planar central configurations correct?

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The \(n\)-body problem and mutual distances

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Euler configurations and quasi-polynomial systems

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Symmetry of planar four-body convex central configurations

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Finiteness of central configurations of five bodies in the plane

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The symmetric central configurations of the 4-body problem with masses \(m_1 = m_2 \neq m_3 = m_4\)

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Central configurations of four bodies with one inferior mass

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Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body Problem

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Relative equilibria of the \((1+N)\)-vortex problem

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Linear instability of relative equilibria for \(n\)-body problems in the plane

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Morse theory indomitable

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On Clustering in Central Configurations

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The collinear central configuration of \(n\) equal masses

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On the integral manifolds of the n-body problem

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Stability of Relative Equilibria in the Problem of <i>N</i>+1 Vortices

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On polygonal relative equilibria in the <i>N</i>-vortex problem

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Strictly convex central configurations of the planar five-body problem

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A four-body convex central configuration with perpendicular diagonals is necessarily a kite

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On the existence of central configurations of \(p\) nested \(n\)-gons

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A family of stacked central configurations in the planar five-body problem

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Uniqueness results for co-circular central configurations for power-law potentials

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Central configurations of the planar coorbital satellite problem

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Four-body co-circular central configurations

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Four-body central configurations with adjacent equal masses

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Triple collision in the planar isosceles three body problem

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Some topology of n-body problems

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Collision Singularities in Celestial Mechanics

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Central configurations of four bodies with an axis of symmetry

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Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of N vortices in the plane

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Convex central configurations of the 4-body problem with two pairs of equal adjacent masses

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Central configurations and mutual differences

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Symmetric planar central configurations of five bodies: Euler plus two

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Continua of central configurations with a negative mass in the \(n\)-body problem

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Stacked central configurations: new examples in the planar five-body problem

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Finiteness of kite relative equilibria in the five-vortex and five-body problems

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Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the \(N\)-body problem

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Finiteness of spatial central configurations in the five-body problem

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Finiteness of relative equilibria in the planar generalized \(N\)-body problem with fixed subconfigurations

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Finiteness of relative equilibria of the four-body problem

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Finiteness of stationary configurations of the four-vortex problem

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Relative equilibria in the four-vortex problem with two pairs of equal vorticities

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Permanent Configurations in the n-Body Problem

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Stability of relative equilibria and Morse index of central configurations

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Origin and infinity manifolds for mechanical systems with homogeneous potentials

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Finiteness and bifurcations of some symmetrical classes of central configurations

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On the central configurations of the planar restricted four-body problem

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Central configurations of the five-body problem with equal masses

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Rosette central configurations, degenerate central configurations and bifurcations

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On the number of central configurations in the n-body problem

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New central configurations for the planar 5-body problem

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Triple and quadruple nested central configurations for the planar \(n\)-body problem

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New stacked central configurations for the planar 5-body problem

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Four-body central configurations with some equal masses

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Planar central configuration estimates in the <i>n</i>-body problem

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The integral manifolds of the three body problem

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Triple collision in the collinear three-body problem

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Morse theory and central configurations in the spatial \(N\)-body problem

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Bifurcations of Relative Equilibria in the <i>N</i>-Body and Kirchhoff Problems

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Orbits of the Three-Body Problem Which Pass Infinitely Close to Triple Collision

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Chaotic dynamics near triple collision

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On central configurations

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Linear stability of relative equilibria with a dominant mass

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Relative equilibria with clusters of small masses

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Generic Finiteness for Dziobek Configurations

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Bifurcation of Spatial Central Configurations from Planar Ones

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Existence of symmetric central configurations

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Stationary Configurations of Point Vortices

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Central configurations of the N-body problem via equivariant Morse theory

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Convex four-body central configurations with some equal masses

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Regular Polygon Solutions of the N-Body Problem

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Central configurations for the planar Newtonian four-body problem

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A continuum of relative equilibria in the five-body problem

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Spectral instability of relative equilibria in the planar<i>n</i>-body problem

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LINEAR STABILITY IN THE 1 + N-GON RELATIVE EQUILIBRIUM

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Linear stability of the elliptic Lagrangian triangle solutions in the three-body problem

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Stability of Relative Equilibria in the Planar $n$-Vortex Problem

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Bifurcations of Central Configurations in the Four-Body Problem with Some Equal Masses

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On the role and the properties ofn body central configurations

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Linear stability of the Lagrangian triangle solutions for quasihomogeneous potentials

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Four-body central configurations with one pair of opposite sides parallel

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Symmetry of the restricted \(4+1\) body problem with equal masses

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Linear stability of a self-gravitating ring

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Bifurcation of central configuration in the \(2N+1\) body problem

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On full-rank interval matrices

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Classification of four-body central configurations with three equal masses

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Relative equilibrium solutions in the four body problem

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Central configurations and a theorem of Palmore

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Topology and mechanics. I

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Topology and mechanics. II: The planar \(n\)-body problem

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Mathematical problems for the next century

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The Apsides of General Dynamical Systems

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A note on the two nested regular polygonal central configurations

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Permanent Configurations in the Problem of Five Bodies

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The \(N\)-gon is not a local minimum of \(U^ 2 I\) for \(N \geq{} 7\)

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Central configurations with many small masses

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Isosceles trapezoid central configurations of the Newtonian four-body problem

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Twisted angles for central configurations formed by two twisted regular polygons

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Nested regular polygon solutions for planar \(2N\)-body problems

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Central configurations for \((pN+gN)\)-body problems

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