The Legacy of the Cartwright-Littlewood Collaboration

The uploaded paper (Guckenheimer 2025) explicitly states—summarizing Haiduc’s rigorous, computer‑assisted proof—that for the forced van der Pol flow there are parameter regions (with ε small) where a hyperbolic invariant set (a horseshoe) exists and the remainder of the nonwandering set consists of exactly one repelling and two stable periodic orbits; it also emphasizes structural stability of this picture. It further explains the stroboscopic return map on θ-constant sections and the slow–fast/canard mechanism that produces the strip‑stretching needed for a horseshoe. These points align with the candidate solution’s construction via Fenichel slow manifolds, a stroboscopic map, Conley–Moser horseshoe criteria, and persistence/structural stability. No material contradictions were found. The model omits explicit validated constants/parameter windows (delegated in the paper to Haiduc’s verification), but its outline matches the paper’s claims and proof strategy. See the paper’s discussion of the stroboscopic map φ on θ-constant sections (), its summary of Haiduc’s results (existence of a hyperbolic invariant set and that the rest of the nonwandering set is one repelling and two stable periodic orbits) and structural stability (; ), the canard-induced stretching leading to a horseshoe and Figure 2’s quadrilateral return (), and the GSPT background ensuring slow manifolds ().