On the Novikov problem for dihedral symmetry potentials

2025/05/12 by A. Ya. Maltsev, Maltsev, A. Ya.
Materials Science · Mathematics · #Analytic and geometric function theory #FOS: Physical sciences #Mathematical Physics (math-ph) #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.07657

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Novikov's problem of describing level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. It is shown that quasiperiodic potentials of this type can have open level lines only at a single energy level ε= ε₀ , which brings them close to random potentials on a plane.

Citations

• On the Novikov problem for superposition of periodic potentials
• Dynamical systems around the Rauzy gasket and their ergodic properties
• On the Hausdorff dimension of the Rauzy gasket
• On connectedness of chaotic sections of some 3-periodic surfaces
• Topology of plane sections of periodic polyhedra with an application to\n the Truncated Octahedron
• Characterization of the set of "ergodic directions" in the Novikov's problem of quasi-electrons orbits in normal metals
• Existence and measure of ergodic leaves in Novikov's problem on the semiclassical motion of an electron
• Deviation for interval exchange transformations

Related

• On the level lines of two-layer symmetric potentials
• On the Novikov problem for superposition of periodic potentials
• Geometry of quasiperiodic functions on the plane
• Quasiperiodic functions on the plane and electron transport phenomena
• Characterization of the set of "ergodic directions" in the Novikov's problem of quasi-electrons orbits in normal metals