This is a survey article dedicated to the study of
topological quantities in theory of normal metals discovered in
the works of the authors during the last years. Our results are
based on the theory of dynamical systems on Fermi surfaces. The
physical foundations of this theory (the so-called “Geometric
Strong Magnetic Field Limit”) were found by the school of I. M.
Lifshitz many years ago. Here the new aspects in the topology of
quasiperiodic functions are developed.