Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T04:06:46.114Z Has data issue: false hasContentIssue false

5 - Weak Tangents and Microsets

from Part One - Theory

Published online by Cambridge University Press:  13 October 2020

Jonathan M. Fraser
Jonathan M. Fraser
Affiliation:
University of St Andrews, Scotland
Get access

Summary

One of the most effective ways to bound the Assouad dimension of a set from below is to use weak tangents; an approach pioneered by Mackay and Tyson. Weak tangents are tools for capturing the extremal local structure of a set. In this chapter we explore this connection. We prove Mackay and Tyson's estimate, and a stronger result of Furstenberg which characterises the Assouad dimension entirely in terms of the Hausdorffdimension of weak tangents.

Keywords

weak tangentmicroset
Type
Chapter
Information
Assouad Dimension and Fractal Geometry , pp. 64 - 78
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×