The Projection Method for Computing Multidimensional Absolutely Continuous Invariant Measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC 2 expanding mappingS:Ω→Ω on a bounded region Ω⊂R N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm