Self-similar sets: Projections, sections and percolation

Kenneth Falconer; Xiong Jin

doi:10.1007/978-3-319-57805-7_6

Self-similar sets: Projections, sections and percolation

Kenneth Falconer, Xiong Jin

University of St Andrews

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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 language	English
Pages (from-to)	113-127
Number of pages	15
Journal	Trends in Mathematics
Volume	PartF3
Early online date	25 Aug 2017
DOIs	https://doi.org/10.1007/978-3-319-57805-7_6
Publication status	Published - 2017

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AB - 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.

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Self-similar sets: Projections, sections and percolation

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