Singularity Results for Functional Equations Driven by Linear Fractional Transformations

Kazuki Okamura ()
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Kazuki Okamura: The University of Tokyo

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1316-1328

Abstract: 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.

Keywords: De Rham’s functional equations; Singular measures; Stationary measures; 60G30; 28A78; 28A80 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-013-0516-x

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