99 citations · 354 across the 14 of their papers we have counts for
14 papers
Kowalevski's analysis of the swinging Atwood's machine
Olivier Babelon, Michel Talon, Michel Capdequi Peyranère
We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios where such expansions exist wit…
The quantum Neumann model: refined semiclassical results
Marc Bellon, Michel Talon
We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching wi…
The quantum Neumann model: asymptotic analysis
Marc Bellon, Michel Talon
We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.
Spectrum of the quantum Neumann model
Marc P. Bellon, Michel Talon
We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non trivial integrable model.
Riemann surfaces, separation of variables and classical and quantum integrability
O. Babelon, M. Talon
We show that Riemann surfaces, and separated variables immediately provide classical Poisson commuting Hamiltonians. We show that Baxter's equations for separated variables immedia…
The symplectic structure of rational Lax pair systems
O. Babelon, M. Talon
We consider dynamical systems associated to Lax pairs depending rationnally on a spectral parameter. We show that we can express the symplectic form in terms of algebro--geometric…