BIFURCATIONS OF THE HÉNON MAP WITH ADDITIVE BOUNDED NOISE

The paper introduces and numerically substantiates three correspondences (fold/topology, real→complex eigenvalues/wedge, non-transversality/cascade) for the boundary map of the noisy Hénon system, and proves some structural properties (definition of β, invariance of normal bundles in the smooth case, duality). However, the core correspondences are explicitly left as conjectures or observations beyond the scope of a proof. The model provides proof sketches using positive reach, β-invariance, and λ-lemma arguments, but it relies on unproven or incorrect steps (e.g., forward invariance of N1+∂M under F(M)⊂M, claiming ∂D(A)=∂A, generic projection assumptions) and omits key technical justifications required to turn the sketches into rigorous proofs. Hence, both are incomplete: the paper in formal proofs of the correspondences, the model in mathematical rigor and correct hypotheses.