Stability and Cyclicity of Polycycles in Non-smooth Planar Vector Fields

In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to non-smooth fields piecewise fields, or Filippov systems). The considered here may contain hyperbolic saddles, semi-hyperbolic saddle-nodes and tangential singularities any degree. We determine when the polycycle is stable unstable. prove bifurcation at most one limit cycle in some conditions least for each singularity other conditions.