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We consider the Lifshitz topological transitions and the correspondingchanges in the galvanomagnetic properties of a metal from the point of view ofthe general classification of open electron trajectories arising on Fermisurfaces of arbitrary complexity in the presence of magnetic field. Theconstruction of such a classification is the content of the Novikov problem andis based on the division of non-closed electron trajectories into topologicallyregular and chaotic trajectories. The description of stable topologicallyregular trajectories gives a basis for a complete classification of non-closedtrajectories on arbitrary Fermi surfaces and is connected with specialtopological structures on these surfaces. Using this description, we describehere the distinctive features of possible changes in the picture of electrontrajectories during the Lifshitz transitions, as well as changes in theconductivity behavior in the presence of a strong magnetic field. As it turnsout, the use of such an approach makes it possible to describe not only thechanges associated with stable electron trajectories, but also the most generalchanges of the conductivity diagram in strong magnetic fields.

Lifshitz transitions and angular conductivity diagrams in metals with complex Fermi surfaces