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Hausdorff dimension of attractors for two dimensional Lorenz transformations

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Abstract

A class of transformations on [0, 1]2, which includes transformations obtained by a Poincare section of the Lorenz equation, is considered. We prove that the Hausdorff dimension of the attractor of these transformations equalsz+1 wherez is the unique zero of a certain pressure function. Furthermore we prove that all vertical intersections with this attractor, except of countable many, have Hausdorff dimensionz.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Thomas Steinberger

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  1. Thomas Steinberger
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Correspondence to Thomas Steinberger.

Additional information

Research was supported by Projekt Nr. P11579-MAT of the Austrian Fonds zur Förderung der wissenschaftlichen Forschung.

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Steinberger, T. Hausdorff dimension of attractors for two dimensional Lorenz transformations. Isr. J. Math. 116, 253–269 (2000). https://doi.org/10.1007/BF02773221

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  • DOI: https://doi.org/10.1007/BF02773221

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