Self-similar sets: projections, sections and percolation

Falconer, Kenneth John; Jin, Xiong

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Date

2017

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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.

Citation

Falconer , K J & Jin , X 2017 , Self-similar sets: projections, sections and percolation . in J Barral & S Seuret (eds) , Recent Developments in Fractals and Related Fields. FARF3 2015 . Trends in Mathematics , Birkhäuser , Cham , pp. 113-127 , Fractals and Related Fields III , île de Porquerolles , France , 19/09/15 . https://doi.org/10.1007/978-3-319-57805-7_6

conference

Publication

Recent Developments in Fractals and Related Fields. FARF3 2015

DOI

https://doi.org/10.1007/978-3-319-57805-7_6

ISSN

2297-0215

Type

Conference item

Rights

© 2017, Springer International Publishing AG. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at link.springer.com / https://doi.org/10.1007/978-3-319-57805-7_6

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/11629