The simplest random iterated function systems are obtained by taking a linear (or, in higher dimensions, affine) iterated function system, and then randomize the translations. They were investigated, in particular, by Jordan, Pollicott, and Simon, Jordan and Jurga, and others. We are going to investigate the second simplest version, in which we are randomizing the contractions, with the goal of obtaining the almost sure value of Hausdorff dimension of the attractor. In the linear situation this question was investigated by Koivusalo, we are considering the higher-dimensional case. However, we are only able to solve the case of diagonal matrices.

This is a joint work with Balázs Bárány and Antti Käenmäki.
Meeting ID: 852 4277 3200 Passcode: 103121