Iskander Taimanov

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:
Huang Y. C., Taimanov I. A.
The Ozawa Solution to the Davey – Stewartson II Equations and Surface Theory
2025, vol. 30, no. 4, pp. 612-617
Abstract
We describe the Ozawa solution to the Davey – Stewartson II equation from the
point of view of surface theory by presenting a soliton deformation of surfaces which is ruled
by the Ozawa solution. The Ozawa solution blows up at a certain moment and we describe
explicitly the corresponding singularity of the deformed surface.
|
Kordyukov Y. A., Taimanov I. A.
Trace Formula for the Magnetic Laplacian on a Compact Hyperbolic Surface
2022, vol. 27, no. 4, pp. 460-476
Abstract
We compute the trace formula for the magnetic Laplacian on a compact hyperbolic
surface of constant curvature with a constant magnetic field for energies above the Mane critical
level of the corresponding magnetic geodesic flow. We discuss the asymptotic behavior of the
coefficients of the trace formula when the energy approaches the Mane critical level.
|
Taimanov I. A.
On an Integrable Magnetic Geodesic Flow on the Two-torus
2015, vol. 20, no. 6, pp. 667-678
Abstract
The magnetic geodesic flow on a flat two-torus 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, nos. 4-5, pp. 598-605
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. 84-100
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.
|