Distortion elements in group of diffeomorphisms of the 2-sphere

The uploaded paper (Conejeros, 2020) states and proves exactly the claim: every distortion element in Diff^1_0(S^2) with a positively recurrent, non-fixed point is an irrational pseudo-rotation, see the abstract and Theorem A, and the detailed proof using the spread machinery (à la Franks–Handel) and Le Calvez–Tal’s horseshoe criteria (Theorems 2.3–2.5) together with a key uniqueness-of-rotation-number proposition for the blown-up annulus, Proposition 3.1 . The proof of Theorem A splits into cases (≥3 fixed points and exactly 2 fixed points), deriving a contradiction via a forced topological horseshoe in the first case (using Corollary 2.2 and Remark 1 on entropy/periodic points) and establishing unique, irrational rotation number in the second case . By contrast, the model’s Step 1 incorrectly claims that the Krylov–Bogolyubov limit measure built from a recurrent non-fixed point cannot be supported on periodic points; recurrence alone does not ensure that the empirical measures’ supports avoid periodic orbits. Moreover, the model’s Step 3–4 rely on annulus rotation forcing (Swanson; Franks’ generalizations of Poincaré–Birkhoff) without verifying required intersection-type hypotheses and continuity properties in the needed generality. The paper’s argument is logically complete within the stated framework; the model’s proof outline has critical gaps.