Quadratic rational functions with a rational periodic critical point of period $3$
作者: Solomon Vishkautsan
刊名: Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.49-79
来源数据库: The Center for Diffusion of Academic Mathematical Journals
DOI: 10.5802/jtnb.1068
关键词: Rational functionsPreperiodic pointsPreperiodicity graphsModuli curves
原始语种摘要: 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 rational 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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  • rational 有理数
  • periodic 周期的
  • point 
  • affine 仿射的
  • critical 临界的
  • satisfying 饱和
  • curve 弯曲
  • exactly 正确地
  • conditions 条件式
  • above 在上面