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arXiv · 1711.06345

Quadratic rational functions with a rational periodic critical point of period 3

Solomon Vishkautsan·Michael Stoll
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Abstract

We provide a complete classification of possible graphs of rational preperiodic points of quadratic rational functions defined over the rationals with a rational periodic critical point of period 3, under two assumptions: that these functions have no periodic points of period at least 5 and the conjectured enumeration of points on a certain genus 6 affine plane curve. We show that there are exactly six such possible graphs, and that rational functions satisfying the conditions above have at most eleven rational preperiodic points.

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Solomon Vishkautsan, Michael Stoll. 2017-11-16. Quadratic rational functions with a rational periodic critical point of period 3. https://arxiv.org/abs/1711.06345

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