On the existence, stability, and structure of periodic bifurcating sets of periodic differential equations.

This paper concerns the bifurcation problem from equilibrium to invariant s-compact periodic sets in Rx R^n, for one parameter families of periodic ordinary differential equations. The analysis is accomplished by using appropriate families of discrete autonomous dynamical systems and some previous results of the authors on the relationship between conditional and unconnditional stability properties of sets in Rx R^n. Detailed information on the structure of the bifurcating sets in one and two dimensions is also obtained.