Sixty years of fractal projections

Kenneth John Falconer; Jonathan Macdonald Fraser; Xiong Jin

doi:10.1007/978-3-319-18660-3

Sixty years of fractal projections

Kenneth John Falconer, Jonathan Macdonald Fraser, Xiong Jin

Pure Mathematics

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

Abstract

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.

Original language	English
Title of host publication	Fractal Geometry and Stochastics V
Editors	Cristoph Bandt, Kenneth J. Falconer, Martina Zähle
Place of Publication	Basel
Publisher	Birkhauser
Pages	3-25
Number of pages	23
ISBN (Electronic)	9783319186603
ISBN (Print)	9783319186597
DOIs	https://doi.org/10.1007/978-3-319-18660-3 https://doi.org/10.1007/978-3-319-18660-3_1
Publication status	Published - 31 Jul 2015
Event	Fractal Geometry and Stochastics V - Tabarz, Germany Duration: 24 Mar 2014 → 29 Mar 2014

Publication series

Name	Progress in Probability
Volume	70
ISSN (Print)	1050-6977

Conference

Conference	Fractal Geometry and Stochastics V
Country/Territory	Germany
City	Tabarz
Period	24/03/14 → 29/03/14

Keywords

Fractals
Projections
Dimensions
Measure

Access to Document

1411.3156
Copyright Springer International Publishing Switzerland 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18660-3_1
Accepted author manuscript, 506 KB

http://arxiv.org/pdf/1411.3156.pdf

Cite this

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AU - Fraser, Jonathan Macdonald

AU - Jin, Xiong

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AB - Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.

KW - Fractals

KW - Projections

KW - Dimensions

KW - Measure

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UR - https://www.scopus.com/pages/publications/85118445791

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BT - Fractal Geometry and Stochastics V

A2 - Bandt, Cristoph

A2 - Falconer, Kenneth J.

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T2 - Fractal Geometry and Stochastics V

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ER -

Sixty years of fractal projections

Abstract

Publication series

Conference

Keywords

Access to Document

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Cite this