Preprint D9/2005
Sectional-hyperbolic systems
Carlos Morales | Metzger, Roger
Keywords: Partially Hyperbolic Set | Attractor | Flow
We introduce a class of vector fields on $n$-manifolds containing the singular-hyperbolic systems on $3$-manifolds \cite{mpp1}, the multidimensional Lorenz attractors \cite{bpv} and the $C^1$-robustly transitive singular sets in \cite{lgw}. We prove that a system in this class cannot be approximated by ones exhibiting non-hyperbolic closed orbits (this property is false for higher-dimensional singular-hyperbolic systems \cite{ts}). Existence of SRB measures and stochastic stability for attractors in the introduced class is discussed.