STATIONARY BIFURCATION TO LIMIT-CYCLES AND HETEROCLINIC CYCLES

We consider stationary bifurcations with Z4.Z2(4) symmetry. For an open set of cubic coefficients in the normal form, we prove the existence of a limit cycle with frequency approximately \lambda\-1 as lambda --> 0. It is shown that there are two types of structurally stable heteroclinic cycles in this example, one of which is of a new type. We find the stability of all of the zeros and heteroclinic cycles which branch from the origin at the bifurcation. Novel techniques are needed for the calculation of stability for the new type of heteroclinic cycle, and the proof of existence of the limit cycles.