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E. C. Zeeman [2] described the behaviour of the iterates of the difference equation $x_{n+1}=R(x_n,x_{n-1},...,x_{n-k})/Q(x_n,x_{n-1},...,x_{n-k})$, n ≥ k, R,Q polynomials in the case $k=1,Q=x_{n-1}$ and $R=x_n+\alpha$, $x_1,x_2$ positive, α nonnegative. We generalize his results as well as those of Beukers and Cushman on the existence of an invariant measure in the case when R,Q are affine and k = 1. We prove that the totally invariant set remains residual when the coefficients vary.