Intermediate dimensions - a survey

Kenneth John Falconer

doi:10.1007/978-3-030-74863-0_14

Intermediate dimensions - a survey

Kenneth John Falconer

Pure Mathematics

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

Abstract

This article surveys the θ-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when θ=0 to box-counting dimensions when θ=1. We bring together diverse properties of intermediate dimensions which we illustrate by examples.

Original language	English
Title of host publication	Thermodynamic Formalism
Subtitle of host publication	CIRM Jean-Morley Chair, Fall 2019
Editors	Mark Pollicott, Sandro Vaienti
Place of Publication	Cham
Publisher	Springer
Pages	469-493
Number of pages	20
ISBN (Electronic)	9783030748630
ISBN (Print)	9783030748623
DOIs	https://doi.org/10.1007/978-3-030-74863-0_14
Publication status	Published - 2021

Publication series

Name	Lecture Notes in Mathematics
Volume	2290
ISSN (Print)	0075-8434
ISSN (Electronic)	0075-8434

Keywords

Hausdorff dimension
Box-counting dimension
Intermediate dimensions

Access to Document

10.1007/978-3-030-74863-0_14

IntermediateSurvey30-12-20
Copyright © 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG 2021. 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_14
Accepted author manuscript, 581 KBLicence: Unspecified

Cite this

@inproceedings{21e4904dfa9a41d99f882dd13ff99a7e,

title = "Intermediate dimensions - a survey",

abstract = "This article surveys the θ-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when θ=0 to box-counting dimensions when θ=1. We bring together diverse properties of intermediate dimensions which we illustrate by examples.",

keywords = "Hausdorff dimension, Box-counting dimension, Intermediate dimensions",

author = "Falconer, {Kenneth John}",

note = "Funding: The work was supported in part by an EPSRC Standard Grant EP/R015104/1.",

year = "2021",

doi = "10.1007/978-3-030-74863-0_14",

language = "English",

isbn = "9783030748623",

series = "Lecture Notes in Mathematics",

publisher = "Springer",

pages = "469--493",

editor = "Mark Pollicott and Sandro Vaienti",

booktitle = "Thermodynamic Formalism",

address = "Netherlands",

}

TY - GEN

T1 - Intermediate dimensions - a survey

AU - Falconer, Kenneth John

N1 - Funding: The work was supported in part by an EPSRC Standard Grant EP/R015104/1.

PY - 2021

Y1 - 2021

N2 - This article surveys the θ-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when θ=0 to box-counting dimensions when θ=1. We bring together diverse properties of intermediate dimensions which we illustrate by examples.

AB - This article surveys the θ-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when θ=0 to box-counting dimensions when θ=1. We bring together diverse properties of intermediate dimensions which we illustrate by examples.

KW - Hausdorff dimension

KW - Box-counting dimension

KW - Intermediate dimensions

UR - https://arxiv.org/abs/2011.04363

U2 - 10.1007/978-3-030-74863-0_14

DO - 10.1007/978-3-030-74863-0_14

M3 - Conference contribution

SN - 9783030748623

T3 - Lecture Notes in Mathematics

SP - 469

EP - 493

BT - Thermodynamic Formalism

A2 - Pollicott, Mark

A2 - Vaienti, Sandro

PB - Springer

CY - Cham

ER -

Intermediate dimensions - a survey

Abstract

Publication series

Keywords

Access to Document

Other files and links

Fingerprint

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this

Intermediate dimensions - a survey

Abstract

Publication series

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this