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math.DS2009
Cubic polynomials with periodic cycles of a specified multiplier
Patrick Ingram
We consider cubic polynomials f(z)=z^3+az+b defined over the function field C(L), with a marked point of period N and multiplier L. In the case N=1, there are infinitely many such…
math.DS2009
On Poonen's Conjecture Concerning Rational Preperiodic Points of Quadratic Maps
Benjamin Hutz, Patrick Ingram
The purpose of this note is give some evidence in support of conjectures of Poonen, and Morton and Silverman, on the periods of rational numbers under the iteration of quadratic po…