p-ADIC ALTERNATED JULIA SETS

The paper’s Theorem 5.4 (equating the alternated filled Julia set with Qp(F) for F = F2∘F1) is essentially correct, though its proof is terse; the model gives a precise and valid argument establishing z2n = F^n(z0) and using that polynomials map bounded sets to bounded sets, so Part (1) is correct for both, with the model’s proof clearer (see Theorem 5.4 in the paper ). However, the paper’s Theorem 5.5 asserts that, under deg(F) ≤ p and |coefficients|p ≤ 1, the alternated p-adic filled Julia set is connected in Cp; this conclusion is false in the usual p-adic topology (closed disks in Cp are totally disconnected). A simple counterexample is F(z) = z^2, for which Qp(F) is the closed unit ball, which is not connected in Cp; nevertheless, the paper deduces connectedness from the parameter-space poly-disk statement (Theorem 4.5) without justification, which is invalid (see Theorems 4.5 and 5.5 ). The model correctly identifies and explains this flaw and notes the likely intended Berkovich interpretation.