CONVERGENCE OF ITERATES IN NONLINEAR PERRON-FROBENIUS THEORY

The paper’s Theorem 3.2 states exactly the claim under review: if f:intC→intC is subhomogeneous and type K order-preserving, has an interior fixed point, and the orbit closure is compact, then the iterates converge to a fixed point. The proof relies on nonexpansiveness in Thompson’s metric and the fact that f acts as an invertible isometry on the ω-limit set, followed by a maximal-distance/perturbation (f_ε = f − ε id) argument to show the ω-limit set is a singleton . The candidate solution outlines the same skeleton: order-interval trapping and nonexpansiveness in Thompson’s metric, type K implying strong order, and then cites Lins (2022) for the convergence theorem, which is precisely Theorem 3.2 in the paper . Minor omissions include not explicitly invoking the “isometry on ω-limit sets” step or the f_ε trick; however, the logic and assumptions match the paper, and no contradictory claims are made.