# Newly reducible iterates in families of quadratic polynomials

@article{Chamberlin2012NewlyRI, title={Newly reducible iterates in families of quadratic polynomials}, author={K. Chamberlin and Emma Colbert and Sharon Frechette and Patrick Hefferman and R. Jones and S. Orchard}, journal={Involve, A Journal of Mathematics}, year={2012}, volume={5}, pages={481-495} }

For fixed n 3 and nearly all values of , we show that there are only finitely many m such that g; m has a newly reducible n-th iterate. For nD 2 we show a similar result for a much more restricted set of . These results complement those obtained by Danielson and Fein (Proc. Amer. Math. Soc. 130:6 (2002), 1589‐1596) in the higher-degree case. Our method involves translating the problem to one of finding rational points on certain hyperelliptic curves, determining the genus of these curves, and… CONTINUE READING

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