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arXiv · 0909.5408

Cubic polynomials with periodic cycles of a specified multiplier

Patrick Ingram
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Abstract

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 objects, and in the case N>2, only finitely many. The case N=2 has particularly rich structure, and we are able to describe all such cubic polynomials defined over the field obtained by adjoining to C the mth roots of L, for all L.

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Patrick Ingram. 2009-09-29. Cubic polynomials with periodic cycles of a specified multiplier. https://doi.org/10.4153/cjm-2011-093-8

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