Minimal models for rational functions in a dynamical setting

Details Minimal models for rational functions in a dynamical setting Minimal models for rational functions in a dynamical setting

2012-04-23

arxiv.org/abs/1204.4967v1

Mathematics

Number Theory

18 pages

Scientific paper

We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational coefficients that have many integers in a single orbit. We find several minimal quadratic rational functions with 8 integers in an orbit and several minimal cubic rational functions with 10 integers in an orbit. We also make some elementary observations on possibilities of an analogue of Szpiro's conjecture in a dynamical setting and on the structure of the set of minimal models for a given rational function.

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