Abstract Given two rational maps f, g: P¹ P¹ of degree d over C, DeMarco, Krieger, and Ye Common preperiodic points for quadratic polynomials. J. Mod. Dyn. 18 (2022), 363–413 have conjectured that there should be a uniform bound B = B (d) > 0 such that either they have at most B common preperiodic points or they have the same set of preperiodic points. We study their conjecture from a statistical perspective and prove that the average number of shared preperiodic points is zero for monic polynomials of degree d 6 with rational coefficients. We also investigate the quantity ₗ {ₐ} (hf (x) + hg (x) ) for a generic pair of polynomials and prove both lower and upper bounds for it.
Ang et al. (Mon,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: