Help1:=proc(): print(`SSSn(f,x)`):end:



#SSSn(f,x): given a function f of x, finds the stable steady states of the discrete 1D dynamical system
#x(n+1)=f(x(n)), and their basin of attraction. Try:
#SSSn((1+x)/(2+x),x);
SSSn:=proc(f,x) local f1,A,a,S:
     f1:=normal(diff(f,x)):
    A:=evalf([solve({x=f},{x})]):
    A:=[seq(subs(A[a],x),a=1..nops(A))];
    S:={}:
    print(`The steady states are`, A):
    for a from 1 to nops(A) do
    if  abs(subs(x=A[a],f1))<1 then
      S:=S union {A[a]}:
    fi:
   od:
   S:
   end: