General finite type IFS and \(M\)-matrix (Q819555)

The authors generalize the concept finite type IFS used to study the Hausdorff dimension of self-similar sets without open set condition (OSC). By applying the \(M\)-matrix theory (an \(M\)-matrix is a matrix whose entries are finite sets of mappings on \(\mathbb{R}^d\)), the authors define the general finite type IFS, removed in this way some restrictions for IFS. It is calculated the Hausdorff dimension of the associated attractors of a family of IFS with three parameters, without OSC.