Self-similar measures associated to a homogeneous system of three maps

2020/10/02 by Ariel Rapaport, Rapaport, Ariel, Péter P. Varjú +1 · 3 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #advanced mathematical theories #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2010.01022

Abstract

We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on \bf R and other more general IFS's. We extend some of the theory recently developed for Bernoulli convolutions to this setting. In the setting of three maps a new phenomenon occurs, which has been highlighted by recent examples of Baker, and Bárány, Käenmäki. To overcome the difficulties stemming form these, we develop novel techniques, including an extension of Hochman's entropy increase method to a function field setup.

Cited by

• Entropy rates in the dimension theory of self-similar measures
• On exponential separation of analytic self-conformal sets on the real line
• Some remarks on the exponential separation and dimension preserving approximation for sets and measures

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