Some Results On The Flynn-Poonen-Schaefer Conjecture

Shalom Eliahou, Youssef Fares

For $c\in \mathbb{Q}$, consider the quadratic polynomial map ${\phi }_c(x)=x^2-c$. Flynn, Poonen and Schaefer conjectured in 1997 that no rational cycle of ${\phi }_c$ under iteration has len…