Lorenz-Like Chaotic Attractors Revised

We describe some recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors Lambda introduced in [26]: (1) there exists an invariant foliation whose leaves are forward contracted by the flow; (2) there exists a positive Lyapunov exponent at every orbit; (3) attractors in this class are expansive and so sensitive with respect to initial data; (4) they have zero volume if the flow is C-2, or else the flow is globally hyperbolic; (5) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (6) the hitting time associated to a geometric Lorenz attractor satisfies a logarithm law; (7) the rate of large deviations for the physical measure on the ergodic basin of a geometric Lorenz attractor is exponential.