PROOF OF THE C2 MAÑÉ’S CONJECTURE ON SURFACES

The paper proves: (i) for surfaces, the set H2(L) of potentials with hyperbolic Mañé set is C^2-open and dense (Theorem C), and (ii) on H2(L) one can perturb so that the Mañé set becomes a single hyperbolic periodic orbit or hyperbolic singularity, and this property is open (Theorem A ⇒ Corollary B), yielding HP2(L) open and dense in C^2(M,R) (Corollary D). These claims and the definitions of H2(L) and HP2(L) appear explicitly in the manuscript and its abstract (e.g., HP2(L) and Theorem A, Theorem C, and Corollary D are all stated in the paper) . The candidate’s solution reproduces the same combination of results (generic hyperbolicity on surfaces plus the channel/locking step to force a periodic orbit) and correctly notes openness via structural stability/semicontinuity. Hence both are correct and follow substantially the same proof strategy.