Differentiability of hausdorff dimension of the non-wandering set in a planar open billiard

Paul Wright

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    Abstract

    We consider open billiards in the plane satisfying the no-eclipse condition. We show that the points in the non-wandering set depend differentiably on deformations to the boundary of the billiard. We use Bowen's equation to estimate the Hausdorff dimension of the non-wandering set of the billiard. Finally we show that the Hausdorff dimension depends differentiably on sufficiently smooth deformations to the boundary of the billiard, and estimate the derivative with respect to such deformations.
    Original languageEnglish
    Pages (from-to)3993-4014
    Number of pages22
    JournalDiscrete and Continuous Dynamical Systems- Series A
    Volume36
    Issue number7
    DOIs
    Publication statusPublished - Jul 2016

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