Happy birthday dear Rabbit
Period tripling bifurcation is similar to the period doubling one.
You see here how Douady's rabbit appears out of a "single embryo cell" :)
At c = -0.125 + 0.65i on the border of the main cardioid the
attracting fixed point loses its stability with multiplier
λ = exp(2π /3).
You see below this 120 o rotation symmetry of
the critical orbit near the bifurcation point. Unstable period-3 orbit
approch to the fixed point.
After the period tripling bifurcation attracting period-3 orbit and unstable
fixed point (with three whiskers) appear.
Previous: Period doubling bifurcations
Next: Parabollic fixed points and Siegel disk
updated 12 Sep 2013