Self-similar sets: projections, sections and percolation

Kenneth John Falconer; Xiong Jin

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

Self-similar sets: projections, sections and percolation

Kenneth John Falconer, Xiong Jin

Pure Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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
Title of host publication	Recent Developments in Fractals and Related Fields. FARF3 2015
Editors	Julien Barral, Stéphane Seuret
Place of Publication	Cham
Publisher	Birkhäuser
Pages	113-127
Number of pages	15
ISBN (Electronic)	9783319578057
ISBN (Print)	9783319578033
DOIs	https://doi.org/10.1007/978-3-319-57805-7_6
Publication status	Published - 2017
Event	Fractals and Related Fields III - Hôtel IGESA, île de Porquerolles, France Duration: 19 Sept 2015 → 25 Sept 2015 Conference number: 3 http://sites.math.u-pem.fr/farf3/

Publication series

Name	Trends in Mathematics
ISSN (Print)	2297-0215

Conference

Conference	Fractals and Related Fields III
Country/Territory	France
City	île de Porquerolles
Period	19/09/15 → 25/09/15
Internet address	http://sites.math.u-pem.fr/farf3/

Access to Document

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

FARF3-FalconerJin
© 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
Accepted author manuscript, 969 KB

Cite this

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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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DO - 10.1007/978-3-319-57805-7_6

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SN - 9783319578033

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BT - Recent Developments in Fractals and Related Fields. FARF3 2015

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CY - Cham

T2 - Fractals and Related Fields III

Y2 - 19 September 2015 through 25 September 2015

ER -

Self-similar sets: projections, sections and percolation

Abstract

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