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

2017/11/16 by Solomon Vishkautsan, Michael Stoll, Vishkautsan, Solomon +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1711.06345

Abstract

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

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