Abstract
We consider the behavior of classical and quantum oscillations in metals with complex Fermi surfaces near the directions of $\, {\bf B} \, $ corresponding to changes in the topological structure of the dynamical system describing the semiclassical motion of quasiparticles along the Fermi surface. The transitions through the boundaries of change in this structure are accompanied by sharp changes in the picture of oscillations, the form of which depends in the most essential way on the topological type of the corresponding reconstruction. We list here the main features of such changes for all topological types of elementary reconstructions and discuss the possibilities of experimental identification of such types based on these features.
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