Hyperbolic Lifts and Estimates for Overlap Numbers
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We first compute topological overlap numbers in several concrete cases. In particular is obtained a class of Bernoulli convolutions systems which asymptotically are irrational-to-1 on their limit sets. Next, for general conformal iterated function systems and for a class of potentials \(\psi \), we prove an estimate on the box dimension of a measure \(\nu _\psi \) on the limit set, associated to an equilibrium measure \(\mu _\psi \) on the respective hyperbolic lift. Also we study the structure of the families of conditional measures of \(\mu _\psi \) with respect to various fiber partitions, and find relations between them.
KeywordsDynamics of endomorphisms Equilibrium measures Stable foliations Entropies Overlap numbers Bernoulli convolutions Pressure
Mathematics Subject Classification37D20 37D35 37A35 37C70
This work was supported by grant PN-III-P4-ID-PCE-2016-0823 Dynamics and Differentiable Ergodic Theory, from UEFISCDI Romania.