ON A SUFFICIENT CONDITION FOR LINEAR CHAOS

The paper proves chaoticity by invoking an unbounded Hypercyclicity Criterion (its Theorem 3.1) and then constructing dense periodic points via a geometric-series argument; both steps are valid under the stated hypotheses, including closedness of all powers and the AB = I right-inverse on a dense Y ⊆ C^∞(A) . The model’s solution gives an explicit gliding-hump construction of a hypercyclic vector plus the same geometric-series construction for periodic points, also correctly leveraging AB = I, eventual nilpotence of A on Y, the exponential bound on B^n, and closedness of A^n. Hence both are correct; the hypercyclicity parts differ (reference to a criterion versus a direct construction), while the periodic-point argument is essentially the same.