Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points

The paper proves both accessibility (Theorem 1.4) under NW(f)=M and π1(M) non-virtually-solvable, and ergodicity (Theorem 1.3) for all C2 conservative partially hyperbolic diffeomorphisms without periodic points. The proof of Theorem 1.4 uses the HHU trichotomy, rules out su-tori and su-sublaminations with periodic boundary, and then deploys a detailed hyperbolic-leaf/ideal-boundary analysis to exclude a global Es⊕Eu-foliation, yielding accessibility . Theorem 1.3 is established by treating both the accessible case (standard Burns–Wilkinson/Hopf mechanism) and, crucially, the non-accessible case, where the authors produce compact periodic center leaves via classification/leaf-conjugacy and conclude ergodicity . By contrast, the model’s outline for (A) omits the core uniform/non-uniform quasi-geodesic dichotomy and boundary-at-infinity arguments that drive the paper’s contradiction, and its (B) proves ergodicity only when accessibility (hence NW(f)=M and non-solvable π1) already holds, failing to cover the non-accessible scenarios that the paper settles.