Teichmüller space for iterated function systems (Q2888655)

The authors study deformation aspects of families of iterated function systems. They introduce the notion of Teichmüller space for these systems and investigate their topological and metric properties. They show that the boundary of such Teichmüller spaces consists primarily of inhomogeneous systems. Also, by equipping these Teichmüller spaces with different metrics (a Euclidean metric, a hyperbolic metric, and a so-called \(\lambda\)-metric), the authors investigate aspects of continuity for the Hausdorff dimension function arising from the limit sets of the iterated function systems and for the corresponding pressure function with respect to these metrics. They show that the hyperbolic metric and the \(\lambda\)-metric lead to topologies which are stronger than the \(\lambda\)-topology introduced by Roy and Urbański (the latter is non-metrizable).