2D universality of period-doubling bifurcations in 3D conservative reversible mappings

Infinite sequences of period-doubling bifurcations are known to occur generically (i.e. with codimension 1) not only in dissipative 1D systems but also in 2D conservative systems, described by area-preserving mappings. In this paper, we study a 3D volume-preserving, reversible mapping and show that it does possess period 2^m(m=1,2,...) orbits, with stability intervals whose length decreases rapidly, with increasing m. Varying one parameter of the system we find that these orbits always bifurcate out of one another with the usual stability exchange and universal properties of period-doubling sequences of 2D-conservative maps. This raises the interesting question whether these 3D reversible maps possess an analytic integral which would render them essentially 2-dimensional.