ANALYTIC GENERICITY OF DIFFUSING ORBITS IN A PRIORI UNSTABLE HAMILTONIAN SYSTEMS

The paper proves analytic genericity of Arnold diffusion for the stated a priori unstable Hamiltonian model via NHIM persistence, Melnikov-based transversality, the symplectic scattering map with first-order expansion, and a shadowing mechanism, culminating in Theorem 2.3 that yields O(1) action drift for an open/dense set of analytic perturbations . Key ingredients include persistence of the NHIM (Proposition 3.1) , a Melnikov potential with nondegenerate critical points (H3a) , the scattering-map expansion sε = Id + ε J∇L* + O(ε^2) (Proposition 3.3) , and the geometric shadowing result (Theorem 3.5) . The candidate solution follows this same scattering-map mechanism. Two caveats: it (i) overstates genericity as C^ω-open (the paper establishes C^ω-dense and C^3-open) and (ii) invokes a stronger ‘accessibility cone spanning R^d’ condition than the paper’s (H3b), which only requires a nonzero Melnikov gradient at one point .