Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter

Abstract

The paper is devoted to the questions connected with the investigation of the S.P. Novikov problem of the description of the geometry of level lines of quasiperiodic functions on a plane with different numbers of quasiperiods. We consider here the history of the question, the current state of research in this field, and a number of applications of this problem to various physical problems. The main attention is paid to the applications of the results obtained in the field under consideration to the theory of transport phenomena in electron systems.

39 pages, 17 figures, Latex

Cited by in corpus (4)

• A universal bound on Quantum Chaos from Random Matrix Theory
• Open level lines of a superposition of periodic potentials on a plane
• Reconstructions of the electron dynamics in magnetic field and the geometry of complex Fermi surfaces
• Distinctive features of oscillatory phenomena in reconstructions of the topological structure of electron trajectories on complex Fermi surfaces