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On the length of critical orbits of stable quadratic polynomials. (English) Zbl 1268.11155
Summary: We use the Weil bound of multiplicative character sums, together with some recent results of N. Boston and R. Jones, to show that the critical orbit of quadratic polynomials over a finite field of $$q$$ elements is of length $$O(q^{3/4})$$, improving upon the trivial bound $$q$$.

##### MSC:
 11T06 Polynomials over finite fields 37P25 Dynamical systems over finite ground fields 11L40 Estimates on character sums
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##### References:
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