Iskander Taimanov
4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia
Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences
D. Sc., Professor
Corresponding Member of RAS
Author and editor in ICS (ICS series «Contemporary Mathematics», «Computing in Mathematics, Physics and Biology»)
Member of the editorial board of «Regular & Chaotic Dynamics»
Publications:
Taimanov I. A.
On an Integrable Magnetic Geodesic Flow on the Twotorus
2015, vol. 20, no. 6, pp. 667678
Abstract
The magnetic geodesic flow on a flat twotorus with the magnetic field $F=\cos(x)dx \wedge dy$ is completely integrated and the description of all contractible periodic magnetic geodesics is given. It is shown that there are no such geodesics for energy $E \geqslant 1/2$, for $E<1/2$ simple periodic magnetic geodesics form two $S^1$families for which the (fixed energy) action functional is positive and therefore there are no periodic magnetic geodesics for which the action functional is negative.

Taimanov I. A.
Periodic magnetic geodesics on almost every energy level via variational methods
2010, vol. 15, no. 45, pp. 598605
Abstract
For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy level the principle of throwing out cycles gives periodic magnetic geodesics on the critical levels defined by the "thrown out" cycles.

Taimanov I. A.
The type numbers of closed geodesics
2010, vol. 15, no. 1, pp. 84100
Abstract
This is a short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesics.
