On some bifurcations of symmetrical piecewise smooth dynamical systems on the plane

The work examines dynamical systems on the plane, defined by piecewise smooth vector fields depending on two parameters. Dynamical systems used in applications often have various kinds of symmetry. Therefore, it is natural to study bifurcations in such systems. Here we consider vector fields that are invariant under the involution of a plane having a single fixed point. It is assumed that for zero values of the parameters the vector field has a periodic trajectory Г passing through two symmetric stitched saddles and not containing other singular points. We describe the bifurcations of phase portraits in the neighborhood of Г for a generic family of vector fields. In particular, the number and type of periodic trajectories generated from Г when the parameters change has been established.