Cubic polynomials with periodic cycles of a specified multiplier
Dynamical Systems
2019-08-15 v2 Algebraic Geometry
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.
Cite
@article{arxiv.0909.5408,
title = {Cubic polynomials with periodic cycles of a specified multiplier},
author = {Patrick Ingram},
journal= {arXiv preprint arXiv:0909.5408},
year = {2019}
}
Comments
Minor revisions based on referee's suggestions