The \(n\)-centre problem of celestial mechanics for large energies

DOI10.1007/s100970100037zbMath1010.70011arXivmath/0702013OpenAlexW2068937473MaRDI QIDQ1599499

Andreas Knauf

Publication date: 10 June 2002

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702013

zbMATH Keywords

singularitiesHausdorff dimensionsymbolic dynamicstopological entropycelestial mechanicshyperbolic setsmolecular scatteringelectronic potentialthree-dimensional motion\(n\)-centre problemlarge energy

Mathematics Subject Classification ID

Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10)

Related Items (18)

Variational aspects of the two-center problem ⋮ Coulomb planar periodic motion of \(n\) equal charges in the field of \(n\) equal positive charges fixed at a line and constant magnetic field ⋮ Entire parabolic trajectories as minimal phase transitions ⋮ Parabolic solutions for the planar \(N\)-centre problem: multiplicity and scattering ⋮ Symbolic dynamics for the anisotropic \(N\)-centre problem at negative energies ⋮ Symbolic dynamics: from the \(N\)-centre to the \((N+1)\)-body problem, a preliminary study ⋮ Chaotic dynamics in refraction galactic billiards ⋮ The escape rate of a molecule ⋮ Coulomb dynamics of three equal negative charges in field of fixed two equal positive charges ⋮ Scattering parabolic solutions for the spatial \(N\)-centre problem ⋮ Topologically distinct collision-free periodic solutions for the \({N}\)-center problem ⋮ Classical n-body scattering with long-range potentials ⋮ On the integrability of the \(n\)-centre problem ⋮ Variational construction for heteroclinic orbits of the \(N\)-center problem ⋮ The spatial \(N\)-centre problem: scattering at positive energies ⋮ The singular Weinstein conjecture ⋮ Analytic structure of many-body Coulombic wave functions ⋮ The problem of two fixed centers: bifurcation diagram for positive energies

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