Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.
Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.
We investigate the nonautonomous periodic system of ODE’s of the form , where is a -periodic function defined by for , for and the vector fields and are related by an involutive diffeomorphism.
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