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E. C. Zeeman [2] described the behaviour of the iterates of the difference equation , n ≥ k, R,Q polynomials in the case and , 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.
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