Self-similar sets: Projections, sections and percolation

Kenneth Falconer, Xiong Jin

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    Abstract

    We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.

    Original languageEnglish
    Pages (from-to)113-127
    Number of pages15
    JournalTrends in Mathematics
    VolumePartF3
    Early online date25 Aug 2017
    DOIs
    Publication statusPublished - 2017

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