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Typical absolute continuity for classes of dynamically defined measures. (English) Zbl 07496420

The paper focuses on a family of iterated function systems which depend on a real parameter \(\lambda\) and addresses the long standing question of absolute continuity of the associated push-forward measure, answering it in the positive under certain assumptions. The introduction gives an overview of the current state of art and summarises the main results in non-technical terms. This is helpful as the setting of the paper is very general and complete statements of the main results are very elaborate. The work is novel with the key difference to previous results being that the measures \(\mu_\lambda\) on the symbolic space depend on the parameter \(\lambda\) unlike in previous settings where the parameter dependence came only from the natural projection. This paper deserves a detailed read for those who are interested in the subject.

MSC:

37E05 Dynamical systems involving maps of the interval
28A80 Fractals
60G30 Continuity and singularity of induced measures
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