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Published in:
2009 | OriginalPaper | Chapter
Invariant Measures—Computation
Authors : Jiu Ding, Aihui Zhou
Published in: Statistical Properties of Deterministic Systems
Publisher: Springer Berlin Heidelberg
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The computational problem of stationary densities of Frobenius-Perron operators will be studied. First we introduce the classic Ulam’s piecewise constant method and its direct extension to multi-dimensional transformations. Then we study the piecewise linear Markov method proposed by the authors for one-and multidimensional transformations. We present Li’s pioneering work solving Ulam’s conjecture for the Lasota-Yorke class of interval mappings, and the convergence proofs of Ulam’s method for piecewise convex mappings by Miller and for piecewise expanding transformations by Ding and Zhou.