Ergodic theory of Lorenz attractors

In 1963, Lorenz found a kind of strange attractor when he studied a family of ordinary differential equations, which is nowadays called the Lorenz attractors. Later in the 1970s, Guckenheimer et al. constructed a geometric model of Lorenz attractors, which has been an important class of systems in differentiable dynamical systems since then. We survey some ergodic properties of geometric Lorenz attractors, which include characterizations of the ergodic measure space, intermediate entropy and intermediate pressure properties, multifractal analysis theory and large deviations.