IFS on boundaries of homogeneous trees: WQB condition and ultifractal analysis

We study, from the point of view of the multifractal analysis, iterated function systems on totally disconnected spaces, namely, the boundaries of homogeneous trees. In particular, we study in this setting the “weak quasi-Bernoulli” property introduced by Testud [3, 4]. After projection on ℝ or ℝ2, we get new examples of self-similar measures which, being WQB, obey the multifractal formalism for positive q's.