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While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking property that all the orbits are periodic on open sets of the phase space. We give a description of this...
There are a few Lax matrices of the Clebsch system. Poles of the Baker – Akhiezer function determine the class of equivalent divisors on the corresponding spectral curves. According to the Riemann – Roch theorem, each class has a unique reduced representative. We discuss properties of such a...
We study the nonrigid dynamics induced by the standard birational actions ofthe split unitary groups...
We investigate the stability of circular point vortex arrays and theirevolution when their dynamics is governed by the generalisedtwo-dimensional Euler’s equations and the three-dimensionalquasi-geostrophic equations. These sets of equations offer a familyof dynamical models depending...
We discuss a model describing the effects of tidal dissipation on the satellite’s orbitin the two-body problem. Tidal bulges are described in terms of a dumbbell, coupled to the rotation by a dissipative interaction. The assumptions on this dissipative coupling turn out to be crucial in...
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