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arXiv · 2410.08785

Exceptions in the domain of generic absolute continuity of non-homogeneous self-similar measures

Jörg Neunhäuserer
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Abstract

Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional singular non-homogeneous self-similar measures in this domain.

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Jörg Neunhäuserer. 2024-10-11. Exceptions in the domain of generic absolute continuity of non-homogeneous self-similar measures. https://doi.org/10.3934/dcdss.2025152

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