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Русская версия

**Sergey Kryzhevich**

Universitetsky prospekt, 28,

198504, Peterhof, St. Petersburg, Russia,

Saint-Petersburg State University,

The Faculty of Mathematics and Mechanics,

Differential Equations Department

An autonomous discontinuous system, defined by a set of vector fields on a compact manifold is studied. A multigraph, describing possible transitions of trajectories from one cell to another, is constructed. It is shown that there exists a canonical algorithm allowing to reduce this graph to its canonical form which is the same for all topologically conjugated systems of vector fields and persists under perturbations of general systems of vector fields. Bifurcations, leading to changing of the normal form of the corresponding graph, are studied.