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

8 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

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10.1017/S0004972715000441

Cite this

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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.",

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AU - Urbański, Mariusz

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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

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Shrinking targets for nonautonomous dynamical systems corresponding to cantor series expansions

Abstract

Keywords

ASJC Scopus subject areas

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