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Quantum Monodromy in the Isotropic 3-Dimensional Harmonic Oscillator
Irina Chiscop, Holger R. Dullin, Konstantinos Efstathiou +1
The isotropic harmonic oscillator in dimension 3 separates in several different coordinate systems. Separating in a particular coordinate system defines a system of three commuting…
Bifurcations and Monodromy of the Axially Symmetric 1:1:-2 Resonance
Konstantinos Efstathiou, Heinz Hanßmann, Antonella Marchesiello
We consider integrable Hamiltonian systems in three degrees of freedom near an elliptic equilibrium in 1:1:-2 resonance. The integrability originates from averaging along the perio…
Self-consistent Method and Steady States of Second-order Oscillators
Jian Gao, Konstantinos Efstathiou
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator netwo…
Scattering invariants in Euler's two-center problem
Nikolay Martynchuk, Holger R. Dullin, Konstantinos Efstathiou +1
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 pa…