  A physical measure on the attractor of a system describes the statistical
behavior of typical orbits. An example occurs in unimodal dynamics. Namely, all
infinitely renormalizable unimodal maps have a physical measure. For Lorenz
dynamics, even in the simple case of infinitely renormalizable systems, the
existence of physical measures is more delicate. In this article we construct
examples of infinitely renormalizable Lorenz maps which do not have a physical
measure. A priori bounds on the geometry play a crucial role in (unimodal)
dynamics. There are infinitely renormalizable Lorenz maps which do not have a
priori bounds. This phenomenon is related to the position of the critical point
of the consecutive renormalizations. The crucial technical ingredient used to
obtain these examples without a physical measure, is the control of the
position of these critical points.
