  We consider the electric conductivity in normal metals in presence of a
strong magnetic field. It is assumed here that the Fermi surface of a metal has
rather complicated form such that different types of quasiclassical electron
trajectories can appear on the Fermi level for different directions of B. The
effects we consider are connected with the existence of regular (stable) open
electron trajectories which arise in general on complicated Fermi surfaces. The
trajectories of this type have a nice geometric description and represent
quasiperiodic lines with a fixed mean direction in the p-space. Being stable
geometric objects, the trajectories of this kind exist for some open regions in
the space of directions of B, which can be represented by "Stability Zones" on
the unit sphere. The main goal of the paper is to give a description of the
analytical behavior of conductivity in the Stability Zones, which demonstrates
in general rather nontrivial properties.
