Higher order symmetry and bifurcation of the period-2 step-1 accelerator mode in the standard map

The bifurcation process of the period-2 step-1 accelerator mode in the stan dard map has been investigated throughly. The formation of dominant 5-cycle s around the central island and the subsequent period doubling of the centr al island have been analyzed by studying the structure of higher order symm etry lines. The present analysis confirms that analysis of the higher order symmetry structure provides a systematic approach for investigating the hi gher order complex structure in the standard map.