Quasiperiodic functions anddynamical systems in quantum solid state physics

This is a survey article dedicated to the study oftopological quantities in theory of normal metals discovered inthe works of the authors during the last years. Our results arebased on the theory of dynamical systems on Fermi surfaces. Thephysical foundations of this theory (the so-called GeometricStrong Magnetic Field Limit) were found by the school of I. M.Lifshitz many years ago. Here the new aspects in the topology ofquasiperiodic functions are developed.Dedicated to IMPA on the occasion of its 50^th anniversaryThe work of S. P. Novikov is partially supported by theNSF Grant DMS 0072700.