Multifractal analysis of Birkhoff averages for countable Markov maps

Godofredo Iommi, Thomas Jordan

Research output: Contribution to journalArticle (Academic Journal)peer-review

19 Citations (Scopus)
308 Downloads (Pure)


In this paper we prove a multifractal formalism of Birkhoff averages for interval maps with countably many branches. Furthermore, we prove that under certain assumptions the Birkhoff spectrum is real analytic. We also show that new phenomena occur; indeed, the spectrum can be constant or it can have points where it is not analytic. Conditions for these to happen are obtained. Applications of these results to number theory are also given. Finally, we compute the Hausdorff dimension of the set of points for which the Birkhoff average is infinite.

Original languageEnglish
Pages (from-to)2559-2586
Number of pages28
JournalErgodic Theory and Dynamical Systems
Issue number8
Early online date25 Aug 2015
Publication statusPublished - Dec 2015


  • math.DS
  • 37C45


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