Thx a lot for your help on limit but now i try to get limit on derivative... and visibly there is a problem in the following code:

> f := evalc(eval(omega(phi(z)), [z = r*e^(I*theta), a = xi+I*eta]));
> fr := simplify(map(diff, f, r));
> map(limit, r^2*fr, r = infinity);

It was in fact 

phi :=z -> (l*z+a)/(1-l*conjugate(a)*z):

But your solution works weel. 
How Can I get the result just involvling "a","z", "Re", "Im" and "abs" as in the definition of omega?