Scattering invariants in Euler's two-center problem

Abstract

The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an important role both in celestial mechanics and in the microscopic world. In the present paper we study the spatial problem in the case of arbitrary (both positive and negative) strengths of the centers. Combining techniques from scattering theory and Liouville integrability, we show that this spatial problem has topologically non-trivial scattering dynamics, which we identify as scattering monodromy. The approach that we introduce in this paper applies more generally to scattering systems that are integrable in the Liouville sense.

References in corpus (6)

• Non-uniqueness of phase shift in central scattering due to monodromy
• Defect in the Joint Spectrum of Hydrogen due to Monodromy
• The Non-Trapping Degree of Scattering
• Parallel transport along Seifert manifolds and fractional monodromy
• Rotation Forms and Local Hamiltonian Monodromy
• Symbolic Dynamics of Magnetic Bumps

Cited by in corpus (4)

• Hamiltonian monodromy and Morse theory
• Monodromy in Prolate Spheroidal Harmonics
• Quantum Monodromy in the Isotropic 3-Dimensional Harmonic Oscillator
• Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres