Consider the following maps: 1) xn+1 = 2xn(1-xn) 2) xn+1 = (2xn) Mod 1 3) xn+1 = xn(2+xn) If we have initial condition

[answerhappygod]

Consider the following maps:
1)
xn+1 = 2xn(1-xn)
2) xn+1 = (2xn) Mod 1
3) xn+1 = xn(2+xn)
If we have initial conditions u0 and
v0 where u0>v0 .
Which of the above options are order-preserving,
namely, un>vn for any n>0? Also, note
that un (vn) denotes the n-th
iterate of the map starting from the initial condition
x0=u0 (x0=v0 ).