Cubic polynomials with periodic cycles of a specified multiplier

Details Cubic polynomials with periodic cycles of a specified multiplier Cubic polynomials with periodic cycles of a specified multiplier

2009-09-29

arxiv.org/abs/0909.5408v2

Mathematics

Dynamical Systems

Minor revisions based on referee's suggestions

Scientific paper

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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