Singular-hyperbolic connecting lemma
The class of singular-hyperbolic sets is of great interest and contains more objects than that of hyperbolic sets, as for example the Lorenz attractor. Thus, it is important to know what properties of hyperbolic sets can be transported to singular-hyperbolic sets. In this work the authors extend the Sectional-Anosov Connecting Lemma presented in [\textit{S. Bautista} and \textit{C. Morales}, Ergodic Theory Dyn. Syst. 30, No. 2, 339--359 (2010; Zbl 1200.37026)] to singular-hyperbolic sets that contain the unstable manifolds of their hyperbolic subsets (this occurs for Lyapunov stable sets, for example). They do so by removing attraction assumptions (note that singular-hyperbolic sets are not attracting sets, in general). Furthermore, they extend this result to compact manifolds with dimension greater than or equal to three, when the singular-hyperbolic set has codimension one.
scientific article; zbMATH DE number 7259121