74
3 Area-Preserving Maps
Fig. 3.15 Period-doubling of
the period 1 elliptic fixed
point of the quadratic map:
(a) a = 0.95, (b) a = 2.98,
(c) a = 3.02 (Bountis 1981)
3.6.3 Scaling in the Quadratic de Vogelaere Map
It is somewhat easier to follow the behavior of the period-doubling bifurcation for
the de Vogelaere (1958) form of the quadratic map, V p , which is defined as
3 Area-Preserving Maps
Fig. 3.15 Period-doubling of
the period 1 elliptic fixed
point of the quadratic map:
(a) a = 0.95, (b) a = 2.98,
(c) a = 3.02 (Bountis 1981)
3.6.3 Scaling in the Quadratic de Vogelaere Map
It is somewhat easier to follow the behavior of the period-doubling bifurcation for
the de Vogelaere (1958) form of the quadratic map, V p , which is defined as