On the Novikov problem with a large number of quasiperiods and its generalizations

Abstract

The paper considers the Novikov problem of describing the geometry of level lines of quasi-periodic functions on the plane. We consider here the most general case, when the number of quasi-periods of a function is not limited. The main subject of investigation is the arising of open level lines or closed level lines of arbitrarily large sizes, which play an important role in many dynamical systems related to the general Novikov problem. As can be shown also, the results obtained for quasiperiodic functions on the plane can be generalized to the multidimensional case. In this case, we are dealing with a generalized Novikov problem, namely, the problem of describing level surfaces of quasiperiodic functions in a space of arbitrary dimension. Like the Novikov problem on the plane, the generalized Novikov problem plays an important role in many systems containing quasiperiodic modulations.

arXiv comment15 pages, 4 figures, latex

References in corpus (14)

• Bose-Einstein Condensates in Optical Quasicrystal Lattices
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Quantum quasicrystals of spin-orbit coupled dipolar bosons
• Dynamical Systems, Topology and Conductivity in Normal Metals in strong magnetic fields
• Topological Phenomena in Normal Metals
• Dynamical Systems, Topology and Conductivity in Normal Metals
• Geometry of plane sections of the infinite regular skew polyhedron {4,6|4}
• Metal-Insulator Transition in Graphene on Boron Nitride
• Diffusion for chaotic plane sections of 3-periodic surfaces
• Topology of quasiperiodic functions on the plane
• Symmetric interval identification systems of order three
• Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas
• Open level lines of a superposition of periodic potentials on a plane
• Features of the motion of ultracold atoms in quasiperiodic potentials