Abstract
Period doubling in three symmetrically coupled two-dimensional area-preserving maps is numerically studied. It is found that there is a two-dimensional manifold on which all period-2n (n=0, 1, 2, . . .) orbits of a period-doubling bifurcation sequence lie. On this manifold, the universality classes of period doubling are just the three classes for two symmetrically coupled two-dimensional area-preserving maps, each characterised by its own Feigenbaum constants, reported by Mao and Helleman (Phys. Rev. A. vol.35, p.1847, 1987). It is also reported that, for three non-symmetrically coupled two-dimensional area-preserving maps, three maps which are fixed under the renormalisation operator have been found. The relevant eigenvalues of perturbation around the fixed maps are again the same as those found for two non-symmetrically coupled two-dimensional area-preserving maps, by Mao and Greene (Phys. Rev. A vol.35, p.3911, 1987). The above-mentioned numerical and renormalisation results for the six-dimensional maps agree with each other.