Sequence of global period doubling bifurcation in the Hénon maps

Though the onset of instability is determined by a local and linear property of the system, a region of bifurcated area in the phase space expands gradually when the control parameter increases over the critical threshold. Relative prevalence of the bifurcated orbit is measured in terms of the relative ratio of the area covered by the bifurcated daughter orbit to that of the mother orbit. Power law scaling relation of the growth process of the period doubling bifurcation have been elucidated for the sequence up to the third generation of the period doubling bifurcation of the periodic orbit in the Hénon maps.