A simple approach to rigorous approximation of invariant measures

Details A simple approach to rigorous approximation of invariant measures A simple approach to rigorous approximation of invariant measures

2011-09-11

arxiv.org/abs/1109.2342v2

Mathematics

Dynamical Systems

32 pages, 9 figures

Scientific paper

We decribe a general result on the approximation of fixed points of operators between normed vector spaces allowing an explicit estimation of the error. This result is particularly suited for the approximation of invariant measures in dynamical systems and in particular by the Ulam method. We apply this result to implement an algorithm for the rigorous computation of invariant densities of piecewise expanding maps up to some error in the $L^{1}$ distance. We show how several related computational and numerical issues can be solved and show some computer experiment calculating rigorous approximation of invariant measure and entropy of some one dimensional maps.

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