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Numerical Computation of Hausdorff Dimension

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GCS - Geometry, compatibility and structure preservation in computational differential equations

We show how finite element approximation theory can be combined with theoretical results about the properties of the eigenvectors of a class of linear Perron-Frobenius operators to obtain accurate approximations of the Hausdorff dimension of some invariant sets arising from iterated function systems.

The theory produces rigorous upper and lower bounds on the Hausdorff dimension. Applications to the computation of the Hausdorff dimension of some Cantor sets arising from real and complex continued fraction expansions are described.




This talk is part of the Isaac Newton Institute Seminar Series series.

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