Abstract
Upon the change of the stochastic parameter, the period-3 accelerator mode of the standard map becomes unstable through hypebolic transition with reflection when the residue R goes over the unity, while it undergoes hyperbolic transition with reflection for the residues R becomes negative. The former case is nothing but the period-doubling bifurcation, in which the formation of new periodic orbits are confirmed with the known symmetry analysis. The hyperbolic transition without reflection however, leads to the birth of a pair of period-3 orbits, which can not he identified as the intersection of known symmetry lines. This finding calls for special interests to explore some kind of hidden symmetry for the hyperbolic transition without reflection in the period-3 accelerator modes of the standard map.
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