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Geometry of quasiperiodic functions on the plane
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The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the results obtained for functions with three quasi-periods, which play a very important role in the theory of transport phenomena in metals. In this part, along with previously known results, a number of new results are presented that significantly refine the general description of the picture that arises in this case. New statements are also presented for the case of functions with more than three quasi-periods, which open up approaches to the further study of Novikov's problem in the most general formulation. The role of Novikov's problem in various fields of mathematical and theoretical physics is also discussed.
Forward citations
Cited by 2 Pith papers
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On the Novikov problem for dihedral symmetry potentials
Any smooth quasiperiodic potential with dihedral symmetry D_n (n≥3) and any number of quasiperiods has open level lines at a single energy value at most.
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Analytical approximations of dispersion laws and ultra-complex conductivity diagrams
Higher-order tight-binding terms open a narrow (~1% of bandwidth) energy interval of ultra-complex type-B conductivity diagrams for simple and BCC lattices.
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