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Journal of Statistical Physics

, Volume 177, Issue 3, pp 468–484 | Cite as

Hyperbolic Lifts and Estimates for Overlap Numbers

  • Eugen MihailescuEmail author
Article
  • 24 Downloads

Abstract

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.

Keywords

Dynamics of endomorphisms Equilibrium measures Stable foliations Entropies Overlap numbers Bernoulli convolutions Pressure 

Mathematics Subject Classification

37D20 37D35 37A35 37C70 

Notes

Acknowledgements

This work was supported by grant PN-III-P4-ID-PCE-2016-0823 Dynamics and Differentiable Ergodic Theory, from UEFISCDI Romania.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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