> f:=proc(n,lambda,x0)
>         local pref;
>         if (n = 0) then
>                 x0;
>         else
>                 pref:=f(n-1,lambda,x0);
>                 lambda*pref*(1-pref);
>     fi;
> end;

  f := proc(n, lambda, x0)
local pref;
    if n = 0 then x0
    else pref := f(n - 1, lambda, x0); lambda*pref*(1 - pref)
    end if
end proc

> for lambda from 0.5 to 4 by 0.5 do
>         print(lambda,(lambda-1)/lambda,f(99,lambda,0.5),f(100,lambda,0.5),f(101,lambda,0.5));
> od;
> 

                                    -30                 -30
  0.5, -1.000000000, 0.3099488555 10   , 0.1549744278 10   ,

                       -31
        0.7748721390 10


       1.0, 0., 0.009485759503, 0.009395779870, 0.009307499190


     1.5, 0.3333333333, 0.3333333334, 0.3333333334, 0.3333333334


     2.0, 0.5000000000, 0.5000000000, 0.5000000000, 0.5000000000


     2.5, 0.6000000000, 0.6000000000, 0.6000000000, 0.6000000000


     3.0, 0.6666666667, 0.6885901998, 0.6433012095, 0.6883942899


     3.5, 0.7142857143, 0.8269407063, 0.5008842110, 0.8749972633


                    4.0, 0.7500000000, 0., 0., 0.

> L:=3.5:A:=(L+1)/(2*L):B:=sqrt(L^2-2*L-3)/(2*L):
> print(L,A+B,A-B,f(99,L,0.5),f(100,L,0.5),f(101,L,0.5),f(102,L,0.5));

  3.5, 0.8571428573, 0.4285714287, 0.8269407063, 0.5008842110,

        0.8749972633, 0.3828196839

>