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Properties of measures supported on fat Sierpinski carpets

Published online by Cambridge University Press:  01 June 2006

THOMAS JORDAN and
MARK POLLICOTT
THOMAS JORDAN
Affiliation:
Department of Mathematics, Warwick University, Coventry CV4 7AL, UK (e-mail: tjordan@maths.warwick.ac.uk, mpollic@maths.warwick.ac.uk)
MARK POLLICOTT
Affiliation:
Department of Mathematics, Warwick University, Coventry CV4 7AL, UK (e-mail: tjordan@maths.warwick.ac.uk, mpollic@maths.warwick.ac.uk)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006, pp. 739 - 754
Copyright
2006 Cambridge University Press