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<p>We consider the conjugate equation driven by two families of finite maps on the unit interval satisfying a compatibility condition. This framework contains de Rham’s functional equations. We give sufficient conditions for singularity of the solution with quantitative estimates in the case where the equation is driven by a family of non-affine maps and a family of linear fractional transformations.</p>

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Quantitative Estimates for Singularity for Conjugate Equations Driven by Linear Fractional Transformations

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Kazuki Okamura

摘要

We consider the conjugate equation driven by two families of finite maps on the unit interval satisfying a compatibility condition. This framework contains de Rham’s functional equations. We give sufficient conditions for singularity of the solution with quantitative estimates in the case where the equation is driven by a family of non-affine maps and a family of linear fractional transformations.