PERIODIC ORBITS IN RÖSSLER SYSTEM

The paper rigorously proves: (i) for a=5.25, b=0.2 the Poincaré map has n-periodic points for every n via verified horizontal covering relations N0⇒N1, N1⇒N1, N1⇒N0 (plus a validated 3-cycle), yielding all periods; (ii) for a=4.7, b=0.2 there is an explicit forward-invariant parallelogram A with P(A)⊂A, coverings that force all periods except {2,3,4} inside A, 2- and 4-cycles certified by interval Newton, and a proof that no fundamental 3-cycle exists in A by showing the unique zero of P^3−Id in A is actually a fixed point of P. The candidate solution misstates key proof details: it (a) claims a full topological horseshoe (four coverings) for a=5.25 when the paper verifies a different three-relation scheme; (b) suggests coverings alone yield all periods n≠3 for a=4.7, overlooking that 2 and 4 are obtained by interval Newton; and (c) asserts ‘no zero of P^3−Id in A,’ contradicting the paper’s actual ‘unique zero which is also a fixed point of P’ argument. Hence the paper is correct, but the model’s proof description is incorrect in important respects.