|
%I #2 Sep 29 2006 03:00:00
%S 1,2,4,8,3,6,16,6,5,12,10,12,32,12,10,4,5,7,24,24,20,20,8,8,7,24,10,
%T 14,9,64,24,10,16,14,20,8,18,14,9,48,48,14,20,40,6,48,16,9,40,40,7,18,
%U 48,16,20,16,28,18,9,28
%N Periods of logistic map intervals in order of size.
%C The region of stability for period 8 after the point where period 4 splits in two is from 3.5440903596 to 3.5644072661 or a width of .0203169065. The period 3 cycle starts at 3.8284271247 = 1+sqrt(8) and ends at 3.8414990075, a width of .0130718828. This is less than that of period 8 so it follows it in sequence. The logistic map is just the real part of the Mandelbrot set.
%C The equation f(x)=a*x(1-x), f2(x)=f(f(x)) has a period 3 oscillation whenever 3.82843<a<3.84150.
%D For references see A087046.
%K nonn
%O 1,2
%A Enrico T. Federighi (rico125162(AT)aol.com), Aug 11 2003
|
