Fractal geometry of Bedford-McMullen carpets

Jonathan M. Fraser

doi:10.1007/978-3-030-74863-0_15

Fractal geometry of Bedford-McMullen carpets

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

Abstract

In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as Bedford-McMullen carpets. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.

Original language	English
Title of host publication	Thermodynamic Formalism
Subtitle of host publication	CIRM Jean-Morlet Chair, Fall 2019
Editors	Mark Pollicott, Sandro Vaienti
Publisher	Springer
Chapter	15
Pages	495-516
Number of pages	22
ISBN (Electronic)	9783030748630
ISBN (Print)	9783030748623
DOIs	https://doi.org/10.1007/978-3-030-74863-0_15
Publication status	Published - 2021
Event	Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications - CIRM, Marseille Luminy, France Duration: 9 Dec 2019 → 13 Dec 2019 https://www.chairejeanmorlet.com/2109.html

Publication series

Name	Lecture Notes in Mathematics
Publisher	Springer
Volume	2290
ISSN (Print)	0075-8434
ISSN (Electronic)	1617-9692

Conference

Conference	Thermodynamic Formalism
Country/Territory	France
City	Marseille Luminy
Period	9/12/19 → 13/12/19
Internet address	https://www.chairejeanmorlet.com/2109.html

Keywords

Bedford-McMullen carpet
Self-affine carpet
Self-affine set
Self-affine measure
Hausdorff dimension
Box dimension
Assouad dimension

Access to Document

10.1007/978-3-030-74863-0_15

BMsurvey
Copyright © 2021 the Author(s), under exclusive license to Springer Nature Switzerland AG. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/978-3-030-74863-0_15
Accepted author manuscript, 3.11 MB

https://arxiv.org/abs/2008.10555

Cite this

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title = "Fractal geometry of Bedford-McMullen carpets",

abstract = "In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as Bedford-McMullen carpets. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.",

keywords = "Bedford-McMullen carpet, Self-affine carpet, Self-affine set, Self-affine measure, Hausdorff dimension, Box dimension, Assouad dimension",

author = "Fraser, \{Jonathan M.\}",

note = "The author was supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034). ; Thermodynamic Formalism : Dynamical Systems, Statistical Properties and their Applications ; Conference date: 09-12-2019 Through 13-12-2019",

year = "2021",

doi = "10.1007/978-3-030-74863-0\_15",

language = "English",

isbn = "9783030748623",

series = "Lecture Notes in Mathematics",

publisher = "Springer",

pages = "495--516",

editor = "Mark Pollicott and Vaienti, \{Sandro \}",

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url = "https://www.chairejeanmorlet.com/2109.html",

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T1 - Fractal geometry of Bedford-McMullen carpets

AU - Fraser, Jonathan M.

N1 - The author was supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034).

PY - 2021

Y1 - 2021

N2 - In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as Bedford-McMullen carpets. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.

AB - In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as Bedford-McMullen carpets. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this survey article we discuss some aspects of Bedford-McMullen carpets, focusing mostly on dimension theory.

KW - Bedford-McMullen carpet

KW - Self-affine carpet

KW - Self-affine set

KW - Self-affine measure

KW - Hausdorff dimension

KW - Box dimension

KW - Assouad dimension

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U2 - 10.1007/978-3-030-74863-0_15

DO - 10.1007/978-3-030-74863-0_15

M3 - Conference contribution

SN - 9783030748623

T3 - Lecture Notes in Mathematics

SP - 495

EP - 516

BT - Thermodynamic Formalism

A2 - Pollicott, Mark

A2 - Vaienti, Sandro

PB - Springer

T2 - Thermodynamic Formalism

Y2 - 9 December 2019 through 13 December 2019

ER -

Fractal geometry of Bedford-McMullen carpets

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

New perspectives in the dimension: New perspectives in the dimension theory of fractals

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this

Fractal geometry of Bedford-McMullen carpets

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

New perspectives in the dimension: New perspectives in the dimension theory of fractals

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this