On the restricted $(N + 1)$-body problem on surfaces of constant curvature (Q6042663)

scientific article; zbMATH DE number 7681527

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English	On the restricted $(N + 1)$-body problem on surfaces of constant curvature	scientific article; zbMATH DE number 7681527

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instance of

scholarly article

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title

On the restricted $(N + 1)$-body problem on surfaces of constant curvature (English)

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Journal of Differential Equations

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publication date

3 May 2023

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zbMATH Keywords

ring solution

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nonlinear stability

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bifurcation

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periodic solution

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KAM torus

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/j.jde.2023.03.013

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cites work

Dynamics and bifurcation of passive tracers advected by a ring of point vortices on a sphere

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The restricted three body problem on surfaces of constant curvature

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Stability of the polar equilibria in a restricted three-body problem on the sphere

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Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.

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Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues

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Stability of equilibria and fixed points of conservative systems

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Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2

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Canonical transformations depending on a small parameter

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On the singularities of the curved $n$-body problem

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Relative equilibria in the 3-dimensional curved n-body problem

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On the stability of tetrahedral relative equilibria in the positively curved 4-body problem

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An intrinsic approach in the curved $n$-body problem: the negative curvature case

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The $n$-body problem in spaces of constant curvature. II: Singularities

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Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden

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Invariant tori in Hamiltonian systems with high order proper degeneracy

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Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples

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Equilibrium points in restricted problems on <i>S</i>2 and <i>H</i>2

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Kepler's problem in constant curvature spaces

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The stability of the Lagrange triangular point and a theorem of Arnold

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Introduction to Hamiltonian dynamical systems and the $N$-body problem.

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Introduction to Hamiltonian dynamical systems and the $N$-body problem

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Invariant tori in the lunar problem

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An intrinsic approach in the curved $n$-body problem. The positive curvature case

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Q5815058

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Periodic orbits near bifurcations of codimension two: Classical mechanics, semiclassics and Stokes transitions

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On the stability of an autonomous Hamiltonian system with two degrees of freedom in the case of equal frequencies

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Q4065809

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Periodic Solutions in Hamiltonian Systems, Averaging, and the Lunar Problem

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Identifiers

zbMATH Open document ID

1515.70012

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DOI

10.1016/j.jde.2023.03.013

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6042663

On the restricted \((N + 1)\)-body problem on surfaces of constant curvature (Q6042663)

Statements

Identifiers

Sitelinks

Mathematics(1 entry)