PERIODIC POINTS AND SHADOWING PROPERTY FOR GENERIC LEBESGUE MEASURE PRESERVING INTERVAL MAPS

The uploaded paper’s Theorem 1 states exactly the five claims about Fix(f,k), Per(f,k), and Per(f) for a generic f ∈ Cλ(I) and every k ≥ 1, including Cantor structure and the precise Hausdorff/lower-box/upper-box dimension statements. The paper also records that (Cλ(I), ρ) is complete, enabling the Baire-category framework. The candidate solution cites this theorem directly and notes the standard identity Fix(f,k) = ⋃_{d|k} Per(f,d) and the countable intersection over k to get simultaneity. Hence the model’s solution and the paper are aligned and effectively the same proof strategy via citation to Theorem 1 and Baire-category arguments.