Singularity Results for Functional Equations Driven by Linear Fractional Transformations
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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.
KeywordsDe Rham’s functional equations Singular measures Stationary measures
Mathematics Subject Classification (2010)60G30 28A78 28A80
The author wishes to express his gratitude to his adviser Professor Shigeo Kusuoka for his encouragement, and to the referee for his or her comments.