5 papers
Surfaces in three-dimensional Lie groups
Dmitry A. Berdinsky, Iskander A. Taimanov
We derive the Weierstrass (or spinor) representation for surfaces in three-dimensional Lie groups Nil, \tilde{SL}_2, and Sol with Thurston's geometries and establish the generating…
On the integrability of the n-centre problem
Andreas Knauf, Iskander A. Taimanov
It is known that for centres and positive energies the -centre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy…
Integrability of the n-centre problem at high energies
A. Knauf, I. A. Taimanov
It is shown that for generic configuration of the centres at high energy levels the n-centre problem is completely integrable by using integrals of the motion however it…
Finite gap theory of the Clifford torus
I. A. Taimanov
We construct the spectral curve and the Baker--Akhiezer function for the Dirac operator which corresponds to the Clifford torus via the Weierstrass representation. By constructing…
An example of a jump from chaos to integrability for magnetic geodesic flows
I. A. Taimanov
It is proved that the motion of a charge particle on a hyperbolic oriented two-dimensional surface in a magnetic field given by the volume form of the hyperbolic metric is complete…