Singularity results for functional equations driven by linear fractional transformations

Abstract

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.

14 pages, Title changed, to appear in Journal of Theoretical Probability

Cited by in corpus (3)

• On regularity for de Rham's functional equations
• Some results for conjugate equations
• A new generalization of the Takagi function