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RSolve can't solve non-linear difference eqns?


This may be a naive question.  I am trying to use RSolve within the
DiscreteMath package to solve simple non-linear difference equations of
first order.  While it solves linear equations over high order with ease,
it seems to be rather stuck with with simple nonlinear equations, even
those that clearly don't explode.  For example:

In[1]:= <<DiscreteMath`RSolve`
In[2]:= RSolve[{x[1 + t] == (1/2)(1 - x[t])^2 + x[t], x[0] == 1/2},x[t],t]
Out[2]= RSolve[{x[1 + t] == (1/2)(1 - x[t])^2 + x[t], x[0] == 1/2},x[t],t]

In other words, it just returns my input as output without solving.
I'd appreciate any help.
Amil Dasgupta
Amil Dasgupta 
Department of Economics, Yale University 
P.O. Box 208268, New Haven CT 06520-8268

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