Shrinking targets for nonautonomous dynamical systems corresponding to cantor series expansions

Lior Fishman; Bill Mance; David Simmons; Mariusz Urbański

doi:10.1017/S0004972715000441

Shrinking targets for nonautonomous dynamical systems corresponding to cantor series expansions

Lior Fishman
, Bill Mance
, David Simmons
, Mariusz Urbański

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

12 Scopus citations

Abstract

We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval , viewed as , corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilising our theorem. In particular, we give a Diophantine approximation interpretation of our scheme.

Original language	English
Pages (from-to)	205-213
Number of pages	9
Journal	Bulletin of the Australian Mathematical Society
Volume	92
Issue number	2
DOIs	https://doi.org/10.1017/S0004972715000441
State	Published - 2 Sep 2015
Externally published	Yes

Keywords

Cantor series expansion
Diophantine approximation
Hausdorff dimension
nonautonomous dynamical system
shrinking target scheme

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1017/S0004972715000441

Cite this

@article{480cfdcb7ec84881aae67cbc6f0c5ca1,

title = "Shrinking targets for nonautonomous dynamical systems corresponding to cantor series expansions",

abstract = "We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval , viewed as , corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilising our theorem. In particular, we give a Diophantine approximation interpretation of our scheme.",

keywords = "Cantor series expansion, Diophantine approximation, Hausdorff dimension, nonautonomous dynamical system, shrinking target scheme",

author = "Lior Fishman and Bill Mance and David Simmons and Mariusz Urba{\'n}ski",

note = "Publisher Copyright: {\textcopyright} 2015 Australian Mathematical Publishing Association Inc.",

year = "2015",

month = sep,

day = "2",

doi = "10.1017/S0004972715000441",

language = "English",

volume = "92",

pages = "205--213",

journal = "Bulletin of the Australian Mathematical Society",

issn = "0004-9727",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - Shrinking targets for nonautonomous dynamical systems corresponding to cantor series expansions

AU - Fishman, Lior

AU - Mance, Bill

AU - Simmons, David

AU - Urbański, Mariusz

PY - 2015/9/2

Y1 - 2015/9/2

N2 - We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval , viewed as , corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilising our theorem. In particular, we give a Diophantine approximation interpretation of our scheme.

AB - We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval , viewed as , corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilising our theorem. In particular, we give a Diophantine approximation interpretation of our scheme.

KW - Cantor series expansion

KW - Diophantine approximation

KW - Hausdorff dimension

KW - nonautonomous dynamical system

KW - shrinking target scheme

UR - https://www.scopus.com/pages/publications/84940958577

U2 - 10.1017/S0004972715000441

DO - 10.1017/S0004972715000441

M3 - Article

AN - SCOPUS:84940958577

SN - 0004-9727

VL - 92

SP - 205

EP - 213

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

Shrinking targets for nonautonomous dynamical systems corresponding to cantor series expansions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this