Generic Global Diffusion for Analytic Uncoupled A Priori Unstable Systems

The paper proves generic global diffusion for analytic, uncoupled a priori unstable systems by constructing a scattering-map-based ascending ladder and shadowing a mixed inner/outer pseudo-orbit; its main theorem (Theorem 2.1) states that for a fixed analytic h and an open dense set Gh of analytic potentials g(q,φ,t), and all sufficiently small ε, there is an orbit with I(0) < I− and I(T) > I+ . The model’s solution reproduces this mechanism: persistence of the NHIM, Melnikov splitting, a first-order scattering map Sε(I,φ,s) = (I + ε∂φL* + O(ε2), φ − ε∂IL* + O(ε2), s) , and an iteration scheme combining inner dynamics with scattering to force a monotone drift in I. Differences are mainly expository: the paper crucially exploits the uncoupled structure (zero phase shift; Sε near identity) and uses a non-quantitative shadowing proposition relying on recurrence and measure preservation on the compact NHIM , whereas the model sketches a standard NHIM λ-lemma shadowing and (unnecessarily) asserts O(ε−1) diffusion time, which the paper explicitly avoids estimating . The existence claim and proof strategy are essentially the same; the model’s extra time claim is unsupported but ancillary to correctness on existence.