Ergodic Theory and Dynamical Systems



Properties of measures supported on fat Sierpinski carpets


THOMAS JORDAN a1 and MARK POLLICOTT a1
a1 Department of Mathematics, Warwick University, Coventry CV4 7AL, UK (e-mail: tjordan@maths.warwick.ac.uk, mpollic@maths.warwick.ac.uk)

Article author query
jordan t   [Google Scholar] 
pollicott m   [Google Scholar] 
 

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.

(Received June 23 2004)
(Revised November 29 2004)