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Recent advances in the monodromy theory of integrable Hamiltonian systems
Nikolay Martynchuk, Henk W. Broer, Konstantinos Efstathiou
The notion of monodromy was introduced by J. J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant…
Hamiltonian monodromy and Morse theory
Nikolay Martynchuk, Henk W. Broer, Konstantinos Efstathiou
We show that Hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying Morse theory to the Hamiltonian of the sys…
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…