Bifurcation of limit cycles at infinity in piecewise polynomial systems (Q1698349)

This paper is a contribution to the theory of bifurcations of limit cycles of planar polynomial vector fields. The first result is a recursive algorithm for the computation of the Lyapunov constants at infinity in piecewise polynomial systems with no singular points at infinity. Furthermore, this method is used to study limit cycle bifurcations in cubic polynomial systems. In particular, conditions for simultaneous Hopf bifurcations at the origin and at infinity are established. As an example, the results are applied to a concrete system to show the existence of exactly 11 limit cycles bifurcating from infinity.