Descripción
Resumen:
Consider a continuous family of planar differential systems with a
center at $p$. The period function assigns to each periodic orbit in
the period annulus its period. The problem of bifurcation of critical periodic orbits has been studied and there are three different situations to consider: bifurcations from the center, bifurcations from the interior of the period annulus and bifurcations from the outer boundary of the period annulus. In this talk we deal with the study of bifurcation of critical periodic orbits from the outer boundary for families of potential systems $X_{\mu} = -y\partial_x+V_{\mu}'(x)\partial_y$ where $\mu$ is a $d$-dimensional parameter. We introduce the notion of criticality as an analogous version of the ciclicity in the framework of limit cycles, and we give general criteria in order to bound the criticality at the outer boundary. That is, the maximum number of critical periodic orbits that can emerge or disappear from the outer boundary of the period annulus as we move the parameter $\mu$. This is a joint work with Francesc Mañosas and Jordi Villadelprat.