  The paper is devoted to the applications of the theory of dynamical systems
to the theory of transport phenomena in metals in the presence of strong
magnetic fields. More precisely, we consider the connection between the
geometry of the trajectories of dynamical systems, arising at the Fermi surface
in the presence of an external magnetic field, and the behavior of the
conductivity tensor in a metal in the limit $\, \omega_{B} \tau \rightarrow
\infty $. The paper contains a description of the history of the question and
the investigation of special features of such behavior in the case of the
appearance of trajectories of the most complex type on the Fermi surface of a
metal.
