The problem of two fixed centers: bifurcations, actions, monodromy

DOI10.1016/j.physd.2004.05.006zbMath1098.70515OpenAlexW2065767969WikidataQ56505673 ScholiaQ56505673MaRDI QIDQ1881721

Holger Waalkens, Holger R. Dullin, Peter H. Richter

Publication date: 14 October 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://pure.rug.nl/ws/files/2948383/2004PhysDWaalkens.pdf

zbMATH Keywords

Integrable systemsMonodromyAction variablesTwo-center problem

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Molecular physics (81V55) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10)

Related Items (30)

Variational aspects of the two-center problem ⋮ Rearrangement of energy bands: topological aspects ⋮ Bifurcation analysis of the motion of a cylinder and a point vortex in an ideal fluid ⋮ Hamiltonian systems with detuned 1:1:2 resonance: manifestation of bidromy ⋮ Monodromy of Hamiltonian systems with complexity 1 torus actions ⋮ Homoclinic orbits in the Euler problem of two fixed centers ⋮ Hamiltonian monodromy and Morse theory ⋮ Parallel transport along Seifert manifolds and fractional monodromy ⋮ Dynamical convexity of the Euler problem of two fixed centers ⋮ On families of periodic orbits in the restricted three-body problem ⋮ Orbits in the problem of two fixed centers on the sphere ⋮ An \(n\) center problem as an example of a geodesic billiard map with singularities: Poincaré maps and dynamics ⋮ Euler integral and perihelion librations ⋮ A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy ⋮ Recent advances in the monodromy theory of integrable Hamiltonian systems ⋮ The \(1:\pm 2\) resonance ⋮ Scattering invariants in Euler’s two-center problem ⋮ New integrable two-centre problem on sphere in Dirac magnetic field ⋮ Topologically distinct collision-free periodic solutions for the \({N}\)-center problem ⋮ Geodesics on the ellipsoid and monodromy ⋮ Fractional monodromy: parallel transport of homology cycles ⋮ Eisenhart lift for Euler's problem of two fixed centers ⋮ Classification of perturbations of the hydrogen atom by small static electric and magnetic fields ⋮ Monodromy in non-integrable systems on certain compact classical phase spaces ⋮ On a convex embedding of the Euler problem of two fixed centers ⋮ Global phase portraits of the planar perpendicular problem of two fixed centers ⋮ Nonuniqueness of the Phase Shift in Central Scattering due to Monodromy ⋮ The problem of two fixed centers: bifurcation diagram for positive energies ⋮ Fractional Hamiltonian monodromy from a Gauss–Manin monodromy ⋮ Electron-positron planar orbits in a constant magnetic field

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