Cubic polynomials with periodic cycles of a specified multiplier
arXiv:0909.5408 · doi:10.4153/CJM-2011-093-8
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.
Minor revisions based on referee's suggestions