On the Maslov class rigidity for coisotropic submanifolds

We define the Maslov index of a loop tangent to the characteristic foliation of a coisotropic submanifold as the mean Conley--Zehnder index of a path in the group of linear symplectic transformations, incorporating the "rotation" of the tangent space of the leaf -- this is the standard Lagrangian counterpart -- and the holonomy of the characteristic foliation. Furthermore, we show that, with this definition, the Maslov class rigidity extends to the class of the so-called stable coisotropic submanifolds including Lagrangian tori and stable hypersurfaces.Comment: 18 pages; v2 minor corrections, references update

The role of cosmic rays in magnetic hydrodynamics of interstellar medium

Cosmic ray (CR) propagation in the Galaxy and generally in the cosmic plasma is usually considered in the diffusion approximation. The diffusion is regarded to result from CR scattering due to their interaction with a magnetic and an electric field. In most cases the fields are assumed to be given. Meanwhile, in the Galaxy the CR energy density w sub cr is similar to I eV/cm, i.e., it is comparable with the energy densities of the magnetic field and turbulent motions in the interstellar gas. Therefore, for the Galaxy it becomes necessary to take into account the influence of CR on the gas dynamics and on the magnetic fields in this gas. The simplest way to this is to use the hydrodynamic approximation, but this is possible only on scales greatly exceeding the CR free path lambda before scattering and only for times larger than lambda/v approx. equals lambda/c. One should thus obtain corresponding MHD equations and establish the limits of their applicability