SRB MEASURES FOR PARTIALLY HYPERBOLIC FLOWS WITH MOSTLY EXPANDING CENTER

The paper proves (A) existence of an SRB measure for a C1 flow with a partially hyperbolic attractor and two-dimensional center, and (B) for C2 flows with Gibbs sectionally expanding center, finiteness of SRB/physical measures whose basins cover Lebesgue-a.e. of the topological basin. Its route uses Crovisier–Yang–Zhang’s dominated entropy formulas for empirical limits (Lemmas 3.1–3.2), the no-singularity lemma (Lemma 3.4), and a two-case analysis in Theorem 3.6 that exploits the 2D center having one zero (flow) exponent; for (B) it uses Lemma 4.2 to force a positive non-flow center exponent for any Gibbs u-state, then uniform estimates via the linear Poincaré flow and periodic approximation to obtain finiteness (Theorem 4.9). The candidate solution tracks these same steps, citing the same ingredients and reaching the same conclusions. A minor discrepancy is a likely typo in the paper (“>” where “≥” is intended in the proof of Theorem 3.6), which the model implicitly corrects by using the weak inequality; otherwise, the proofs align closely. See Theorems A/B and the supporting lemmas as stated and proved in the uploaded PDF (e.g., Lemmas 3.1–3.2 and Lemma 3.4; Theorems 3.6, 4.3, 4.9) .