On Shilnikov’s scenario in 3D: Topological chaos for vectorfields of class C1

The paper constructs forward and entire trajectories that realize any prescribed 0–1 itinerary using curve-selection and compactness (Proposition 8.1 and Theorem 8.2), explicitly avoiding 2D covering relations and cone/hyperbolicity checks and noting that periodic orbits remain open; hence, no horseshoe or conjugacy is claimed (and would in fact imply periodic points) . By contrast, the model’s solution asserts Conley–Moser two-strip horseshoe conditions (vertical/horizontal strips, C1 graph level sets with small slopes, cone invariance, diffeomorphic restriction, expansion/contraction) without these derivative and transversality estimates being established in the paper. The paper only proves continuity of the angle map Φj (not C1) and certain separation and boundary-crossing properties (Propositions 6.3, 7.1, 7.3, 7.4), which are insufficient to invoke Conley–Moser . Therefore the model’s proof relies on missing assumptions and over-claims a horseshoe and conjugacy that the paper deliberately does not assert.