3.6 Bifurcation of M-Cycles
77
Fig. 3.17 The neighborhood
of the period 2 orbits of the
quadratic de Vogelaere map
just before they period-double
(p = −1.234) into four
period 4 orbits. (a) Both the
good (left) and bad (right)
points on the dominant
symmetry line. (b)
Magnification of the
neighborhood of the good
point. (c) Magnification of the
neighborhood of the bad
point
lim
k→∞
x
(k)
= x
∗
= −0.23600609
and does it with a convergence rate
˜
α = lim
k→∞
x (k) − x (k−1)
x (k+1) − x (k)
= −4.018076704.
77
Fig. 3.17 The neighborhood
of the period 2 orbits of the
quadratic de Vogelaere map
just before they period-double
(p = −1.234) into four
period 4 orbits. (a) Both the
good (left) and bad (right)
points on the dominant
symmetry line. (b)
Magnification of the
neighborhood of the good
point. (c) Magnification of the
neighborhood of the bad
point
lim
k→∞
x
(k)
= x
∗
= −0.23600609
and does it with a convergence rate
˜
α = lim
k→∞
x (k) − x (k−1)
x (k+1) − x (k)
= −4.018076704.