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We study the critical behavior (CB) of all period $p$-tuplings $(p\!=\!2,3,4,\dots)$ in $N$ $(N \!=\! 2,3,4,\dots)$ symmetrically coupledone-dimensional maps. We first investigate the CB for the $N=2$ case of twocoupled maps, using a renormalization method. Three (five) kinds of fixedpoints of the renormalization transformation and their relevant ``couplingeigenvalues'' associated with coupling perturbations are found in the case ofeven (odd) $p$. We next study the CB for the linear- and nonlinear-couplingcases (a coupling is called linear or nonlinear according to its leading term),and confirm the renormalization results. Both the structure of the critical set(set of the critical points) and the CB vary according as the coupling islinear or nonlinear. Finally, the results of the two coupled maps are extendedto many coupled maps with $N \geq 3$, in which the CB depends on the range ofcoupling.Comment: RevTeX, 30 figures available upon reques

Periodp-tuplings in coupled maps