Self Similar Sets, Entropy and Additive Combinatorics

Michael Hochman*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

This article is an exposition of the main result of [Hoc12], that self-similar sets whose dimension is smaller than the trivial upper bound have "almost overlaps" between cylinders. We give a heuristic derivation of the theorem using elementary arguments about covering numbers. We also give a short introduction to additive combinatorics, focusing on inverse theorems, which play a pivotal role in the proof. Our elementary approach avoids many of the technicalities in [Hoc12], but also falls short of a complete proof; in the last section we discuss how the heuristic argument is turned into a rigorous one.

Original languageAmerican English
Title of host publicationGeometry and Analysis of Fractals
PublisherSpringer New York LLC
Pages225-252
Number of pages28
ISBN (Print)9783662439197
DOIs
StatePublished - 2014
EventInternational Conference on Advances of Fractals and Related Topics - , Hong Kong
Duration: 10 Dec 201214 Dec 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume88
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Advances of Fractals and Related Topics
Country/TerritoryHong Kong
Period10/12/1214/12/14

Bibliographical note

Funding Information:
Supported by ERC grant 306494

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