We consider a class of piecewise hyperbolic maps from the unit square toitself preserving a contracting foliation and inducing a piecewise expandingquotient map, with infinite derivative (like the first return maps of Lorenzlike flows). We show how the physical measure of those systems can berigorously approximated with an explicitly given bound on the error, withrespect to the Wasserstein distance. We apply this to the rigorous computationof the dimension of the measure. We present a rigorous implementation of thealgorithms using interval arithmetics, and the result of the computation on anontrivial example of Lorenz like map and its attractor, obtaining a statementon its local dimension.
展开▼
