  We consider the Lifshitz topological transitions and the corresponding
changes in the galvanomagnetic properties of a metal from the point of view of
the general classification of open electron trajectories arising on Fermi
surfaces of arbitrary complexity in the presence of magnetic field. The
construction of such a classification is the content of the Novikov problem and
is based on the division of non-closed electron trajectories into topologically
regular and chaotic trajectories. The description of stable topologically
regular trajectories gives a basis for a complete classification of non-closed
trajectories on arbitrary Fermi surfaces and is connected with special
topological structures on these surfaces. Using this description, we describe
here the distinctive features of possible changes in the picture of electron
trajectories during the Lifshitz transitions, as well as changes in the
conductivity behavior in the presence of a strong magnetic field. As it turns
out, the use of such an approach makes it possible to describe not only the
changes associated with stable electron trajectories, but also the most general
changes of the conductivity diagram in strong magnetic fields.
