Multifractal analysis for expanding interval maps with infinitely many branches

Ai-Hua Fan, Thomas M Jordan, Lingmin Liao, Michael Rams

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

18 Citations (Scopus)
302 Downloads (Pure)


In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.
Original languageEnglish
Pages (from-to)1847-1870
Number of pages24
JournalTransactions of the American Mathematical Society
Issue numberno. 3
Publication statusPublished - Mar 2015


  • Multifractal analysis
  • Birkhoff averages
  • interval maps
  • infinitely many branches


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