Robust decay for higher-dimensional sectionally-hyperbolic singular flows

Consider smooth singular flows in dimensions higher than three that are sectionally-hyperbolic, meaning that they belong to the higher-dimensional class described in the source, generalizing hyperbolicity for singular flows and including singular-hyperbolic attractors in three-manifolds. The sectional-hyperbolicity conjecture. Such flows exhibit robust exponential decay of correlations. The source presents this as a proposed higher-dimensional extension; sectional-hyperbolicity is described as a generalization containing the three-dimensional singular-hyperbolic case, and the claim remains open.