Iskander Asanovich Taimanov

Integrable geodesic flows with positive topological entropy

An example of a real-analytic metric on a compact manifold whose geodesic flow is Liouville integrable by

On nonformal simply-connected symplectic manifolds

C^infty

The type numbers of closed geodesics

functions and has positive topological entropy is constructed.

The Moutard transformation of two-dimensional Dirac operators and Möbius geometry

For any

Finite-gap theory of the Clifford torus

N geq 5

Periodic magnetic geodesics on almost every energy level via variational methods

nonformal simply connected symplectic manifolds of dimension

On an Integrable Magnetic Geodesic Flow on the Two-torus

2N

Two-dimensional Schrödinger operators with fast decaying potential and multidimensional

are constructed. This disproves the formality conjecture for simply connected symplectic manifolds which was introduced by Lupton and Oprea.

L_2

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.

-kernel

We describe the action of inversion on given Weierstrass representations for surfaces and show that the Moutard transformation of two-dimensional Dirac operators maps the potential (the Weierstrass representation) of a surface S to the potential of a surface