ANOTHER PROOF OF BURGUET’S EXISTENCE THEOREM FOR SRB MEASURES OF C∞ SURFACE DIFFEOMORPHISMS

The uploaded paper (Buzzi–Crovisier–Sarig, 2022) states and proves that for a C^∞ surface diffeomorphism f, if the set of points with limsup_{n→∞} (1/n) log ||Df^n(x)|| > 0 has positive Riemannian area, then f admits an SRB measure; their proof reduces to a curve and uses empirical-measure decompositions and Yomdin-type reparametrization estimates to deduce h(f,μ1)=λ^+(μ1)>0 for an invariant measure μ1, whence an SRB ergodic component exists (see the theorem statement and conclusion with βλ^+(μ1)=λ and λ ≤ β h(f,μ1) implying equality) . The model’s solution instead directly invokes Burguet’s 2021 theorem to obtain existence of an SRB measure and then uses Ledrappier–Young and Ruelle’s inequality to get h(f,μ)=λ^+(μ); this is a different, higher-level proof path that yields the same conclusion. The model additionally asserts an “iff” and basin-covering statement credited to Burguet; the paper notes that Burguet’s method also describes basins, whereas their note focuses on existence, so there is no conflict here .