Closed families of periodic solutions of the restricted three-body problem

The plane circular restricted three-body problem has infinitely many families of symmetric periodic solutions (SPS). Among natural families of SPS, there are some that close upon themselves when the parameter changes (the family $c$, for example). These families preserve this property for all admissible values of the mass parameter $\mu$. There is, however, another type of closed families of SPS that exist only in some intervals of values of $\mu$, and which appear as a result of self-bifurcations of some families of SPS. These type of closed families is poorly understood. In this paper we describe an initial part of an infinite cascade of self-bifurcations of the natural family $i$ (4 bifurcations).