Abstract
We study the critical behavior of period doublings in N symmetrically coupled area-preserving maps for many-coupled cases with Ng3. It is found that the critical scaling behaviors depend on the range of coupling interaction. In the extreme long-range case of global coupling, in which each area-preserving map is coupled to all the other area-preserving maps with equal strength, there exist an infinite number of bifurcation routes in the parameter plane, each of which ends at a critical point. The critical behaviors, which vary depending on the type of bifurcation routes, are the same as those for the previously studied small-N cases (N=2,3), independently of N. However, for any other nonglobal coupling cases of shorter-range couplings, there remains only one bifurcation route ending at the zero-coupling critical point, at which the N area-preserving maps become uncoupled. The critical behavior at the zero-coupling point is also the same as that for the small-N cases (N=2,3), independently of the coupling range.
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