Dynamical Systems, Topology and Conductivity in Normal Metals

New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field ($B \leq 10^{3} Tl$). Our investigation is based on the study of dynamical systems on Fermi surfaces for the motion of semi-classical electron in magnetic field. All possible asymptotic regimes are also found for $B \to \infty$ based on the topological classification of trajectories.Comment: Latex, 51 pages, 14 eps figure

Topological Phenomena in Normal Metals

This paper is devoted to topological phenomena in normal metals with rather complicated Fermi surface. The results of the article are based on the deep topological theorems concerning the geometry of non-compact plane sections of level surfaces of periodic function in 3-dimensional Euclidean space which are the quasi-classical electron orbits in the presence of homogeneous magnetic field. The main result is that the observation of electrical conductivity in strong magnetic fields can reveal such nontrivial topological characteristics of Fermi surface as integral planes, connected with conductivity tensor and locally stable under small rotations of magnetic field. This planes are connected with generic non-closed orbits on the Fermi surface. Some non-generic situations are also discussed.Comment: 21 pages, 9 Encapsulated Postscript figure