The Projection Method for Computing Multidimensional Absolutely Continuous Invariant Measures

Document Type

Article

Publication Date

11-1-1994

Department

Physics and Astronomy

School

Mathematics and Natural Sciences

Abstract

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.

Publication Title

Journal of Statistical Physics

Volume

77

Issue

3-4

First Page

899

Last Page

908

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