2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217060We prove that a singular-hyperbolic attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their orbits coincide. Secondly, there exists a physical (or Sinai-Ruelle-Bowen) measure supported on the attractor whose ergodic basin covers a full Lebesgue (volume) measure subset of the topological basin of attraction. Moreover this measure has absolutely continuous conditional measures along the center-unstable direction, is a $u$-Gibbs state and an equilibrium state for the logarithm of the Jacobian of the time one map of the flow along the strong-unstable direction. This extends to the class of singular-hyperbolic attractors the main elements of the ergodic theory of uniformly hyperbolic (or Axiom A) attractors for flows.55 pages, extra figures (now a total of 16), major rearrangement of sections and corrected proofs, improved introductionDynamical Systems37C10, 37C40, 37D30text