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3 Area-Preserving Maps
Fig. 3.16 Period-doubling
bifurcation of the period 1
fixed point of the quadratic de
Vogelaere map: (a)
p = −0.98, (b) p = −1.02,
(c) p = −1.05
There will always be two members of a period 2 k orbit on the symmetry line y = 0.
When they bifurcate, the period-doubled daughters of one of them will move off the
symmetry line (the “bad” point) as we decrease p, while the daughters of the other
(the “good” point) will remain on the symmetry line. The position, x = x (k) , of the
good point when it bifurcates also accumulates to a fixed value
3 Area-Preserving Maps
Fig. 3.16 Period-doubling
bifurcation of the period 1
fixed point of the quadratic de
Vogelaere map: (a)
p = −0.98, (b) p = −1.02,
(c) p = −1.05
There will always be two members of a period 2 k orbit on the symmetry line y = 0.
When they bifurcate, the period-doubled daughters of one of them will move off the
symmetry line (the “bad” point) as we decrease p, while the daughters of the other
(the “good” point) will remain on the symmetry line. The position, x = x (k) , of the
good point when it bifurcates also accumulates to a fixed value