Lyapunov coefficients for monodromic tangential singularities in Filippov vector fields

In planar analytic vector fields, a monodromic singularity can be distinguished between focus or center by means of the Lyapunov coefficients, which are given in terms power series coefficients first-return map defined around singularity. this paper, we interested an analogous problem for tangential singularities piecewise fields $Z=(Z^+ ,Z^-)$. First, prove that map, neighborhood singularity, is analytic, allows definition coefficients. Then, as consequence general property pair involutions, obtain index first non-vanishing coefficient always even. addition, recursive formula together with Mathematica algorithm computing obtained. We also provide results regarding limit cycles bifurcating from singularities. Several examples analyzed.