**Nurlan Dairbekov
Sobolev Institute of Mathematics, Russia**

*Date:* April 13, 2005

In this talk, we will discuss some results for the integral geometry problem for Anosov magnetic flows. The results are a joint work of the speaker with G. Paternain. We give applications to rigidity problems. The first is a rigidity theorem for contact magnetic flows of surfaces. The second is the action spectra rigidity for magnetic flows and, as a consequence, the eigenvalue rigidity for the twisted Laplacian.