The eventual stability classification for quadratic polynomials with reciprocal integer parameter
Let fr(x)=x2+rf_r(x)=x^2+rfr(x)=x2+r with r=1/cr=1/cr=1/c for c∈Z∖0,−1c\in\mathbb{Z}\setminus\\{0,-1\\}c∈Z∖0,−1. Let C(fr,0)C(f_r,0)C(fr,0) denote the eventual number of irreducible factors of the iterates, and let knk_nkn be the numb…