Exceptions in the domain of generic absolute continuity of non-homogeneous self-similar measures
arXiv:2410.08785 · doi:10.3934/dcdss.2025152
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.