Hard ball systems are completely hyperbolic.
Hard balls gas and Alexandrov spaces of curvature bounded above.
Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations
We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights using the recurrence...