General finite type {IFS} and {$M$}-matrix

In [14], Ngai and Wang introduced the concept of finite type IFS to study the Hausdorff dimension of self-similar sets without open set condition. In this paper, by applying the M-matrix theory([15]), we generalize the notion of finite type IFS to the general finite type IFS. A family of IFS with $3$ parameters, but without open set condition is presented. The Hausdorff dimension of the associated attractors can be calculated by both the $M$-matrix method and the general finite type IFS method. But these IFS are not finite type except for those parameters lying in a set of measure zero.

2010 Mathematics Subject Classification

Primary 28A80. Secondary 37C45.

Full Text (PDF format)

Published 1 January 2005