Bifurcations of links of periodic orbits in non-singular Morse–Smale systems with a rotational symmetry on S3

AbstractIn this paper we consider a rotational symmetry on a non-singular Morse–Smale (NMS) system analyzing the restrictions this symmetry imposes on the links defined by the set of its periodic orbits and to the appearance of local generic codimension one bifurcations in the set of NMS flows on S3. The topological characterization is obtained by writing the involved links in terms of Wada operations.It is also obtained that symmetry implies that in general bifurcations have to be multiple. On the other hand, we also see that there exists a set of links that cannot be related to any other by sequences of this kind of bifurcation