On Wilson’s theorem about domains of attraction and tubular neighborhoods

The paper gives a complete, geometric construction of a global diffeomorphism g: NS → DA via precompact tubular neighborhoods, time-shifts of the flow, and an inductive rectification using isotopy/diffeotopy extension (Propositions 19–20 and Theorem 21), yielding DA diffeomorphic to the normal bundle and hence homeomorphic to a tubular neighborhood. The candidate solution’s Lyapunov-time reparametrization map H relies on an unproven inclusion V^{-1}([0,a0)) ⊂ U0 for a fixed tubular neighborhood U0, and on continuity of the hitting-time map T without ruling out sequences where T(x_n) → ∞ as x_n → S; these gaps prevent the claimed homeomorphism onto a chosen tubular neighborhood.