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Does there exist a rational quadratic polynomial of Sharkovskys type 2-infinity?

I agree with the answer of jc in the case of real polynomial, for this question Does there exist a real quadratic polynomial of Sharkovskys type 2-infinity?

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    $\begingroup$ It is customary over here to invest a certain amount of care in the questions. $\endgroup$ Apr 30, 2011 at 7:18
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    $\begingroup$ This would seem to be a follow-up to mathoverflow.net/questions/63441/… $\endgroup$ Apr 30, 2011 at 8:17
  • $\begingroup$ Here it is quadratic polynomial with rational coefficient. $\endgroup$
    – Aliakbar
    Apr 30, 2011 at 9:16
  • $\begingroup$ Unlikely. All such examples usually involve the Thue-Morse sequence, which usually leads to transcendental numbers. (Its binary sum is transcendental, say.) $\endgroup$ Apr 30, 2011 at 13:07

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