Geometry of quasiperiodic functions on the plane

Abstract

A review of the most recent results obtained in the Novikov problem of the description of the geometry of the level curves of quasiperiodic functions in the plane is presented. Most of the paper is devoted to the results obtained for functions with three quasiperiods, which play a very important role in the theory of transport phenomena in metals. In that part, along with previously known results, a number of new results are presented that refine significantly the general description of the picture arising. New statements are also presented for functions with more than three quasiperiods, which open approaches to further investigations of the Novikov problem in the most general formulation. The role of the Novikov problem in various fields of mathematical and theoretical physics is discussed. Bibliography: 60 titles.