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Properties of measures supported on fat Sierpinski carpets

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Jordan, Thomas and Pollicott, Mark. (2006) Properties of measures supported on fat Sierpinski carpets. Ergodic Theory and Dynamical Systems, Vol.26 (No.3). pp. 739-754. ISSN 0143-3857

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Official URL: http://dx.doi.org/10.1017/S0143385705000696

Abstract

In this paper we study certain conformal iterated function schemes in two dimensions that are natural generalizations of the Sierpinski carpet construction. In particular, we consider scaling factors for which the open set condition fails. For such ‘fat Sierpinski carpets’ we study the range of parameters for which the dimension of the set is exactly known, or for which the set has positive measure.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Fractals, Dimension theory (Topology), Dimensional analysis

Journal or Publication Title:

Ergodic Theory and Dynamical Systems

Publisher:

Cambridge University Press

ISSN:

0143-3857

Official Date:

June 2006

Dates:

Date	Event
June 2006	Published

Volume:

Vol.26

Number:

No.3

Page Range:

pp. 739-754

Identification Number:

10.1017/S0143385705000696

Status:

Peer Reviewed

Access rights to Published version:

Open Access

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