Self-similar sets: projections, sections and percolation

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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
Title of host publicationRecent Developments in Fractals and Related Fields. FARF3 2015
EditorsJulien Barral, Stéphane Seuret
Place of PublicationCham
PublisherBirkhäuser
Pages113-127
Number of pages15
ISBN (Electronic)9783319578057
ISBN (Print)9783319578033
DOIs
Publication statusPublished - 2017
EventFractals and Related Fields III - Hôtel IGESA, île de Porquerolles, France
Duration: 19 Sept 201525 Sept 2015
Conference number: 3
http://sites.math.u-pem.fr/farf3/

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215

Conference

ConferenceFractals and Related Fields III
Country/TerritoryFrance
Cityîle de Porquerolles
Period19/09/1525/09/15
Internet address

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