Hausdorff dimension for fractals invariant under multiplicative integers

Richard Kenyon; Yuval Peres; Boris Solomyak

doi:10.1017/S0143385711000538

Hausdorff dimension for fractals invariant under multiplicative integers

Richard Kenyon, Yuval Peres, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

Abstract

We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences (x k) such that x k x 2k=0 for all k. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts.

Original language	English
Pages (from-to)	1567-1584
Number of pages	18
Journal	Ergodic Theory and Dynamical Systems
Volume	32
Issue number	5
DOIs	https://doi.org/10.1017/S0143385711000538
State	Published - Oct 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Access to Document

10.1017/S0143385711000538

Cite this

@article{10dca2b9b8464013b08cc51df3080549,

title = "Hausdorff dimension for fractals invariant under multiplicative integers",

abstract = "We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences (x k) such that x k x 2k=0 for all k. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts.",

author = "Richard Kenyon and Yuval Peres and Boris Solomyak",

year = "2012",

month = oct,

doi = "10.1017/S0143385711000538",

language = "الإنجليزيّة",

volume = "32",

pages = "1567--1584",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

number = "5",

}

TY - JOUR

T1 - Hausdorff dimension for fractals invariant under multiplicative integers

AU - Kenyon, Richard

AU - Peres, Yuval

AU - Solomyak, Boris

PY - 2012/10

Y1 - 2012/10

N2 - We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences (x k) such that x k x 2k=0 for all k. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts.

AB - We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences (x k) such that x k x 2k=0 for all k. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for multiplicative subshifts.

UR - http://www.scopus.com/inward/record.url?scp=84866028076&partnerID=8YFLogxK

U2 - 10.1017/S0143385711000538

DO - 10.1017/S0143385711000538

M3 - مقالة

SN - 0143-3857

VL - 32

SP - 1567

EP - 1584

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 5

ER -

Hausdorff dimension for fractals invariant under multiplicative integers

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this