The theory of closed 1-forms, levels of quasiperiodic functions and transport phenomena in electron systems

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 \to \infty $. We describe the history of the question and investigate 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.