Elliptic fixed points with an invariant foliation: Some facts and more questions

The paper proves an alternative for each family Fλ, Fλ,•,g, Fλ,f,•: either basic normalizations are always convergent or else normalizations are generically divergent; it then shows generic divergence in two of the families for every irrational ω and, in the third, generic divergence when ω is non‑Brjuno. By contrast, the candidate claims a sharp arithmetic dichotomy—Brjuno implies convergence for every map in each family, non‑Brjuno implies generic divergence—which flatly contradicts the paper’s Theorem 30(i) asserting generic divergence in Fλ and Fλ,•,g for all ω. The model also attributes an “always-convergent” branch to Brjuno without proof in the paper.