Precise asymptotics on the Birkhoff sums for dynamical systems

Lulu Fang, Hiroki Takahasi, Yiwei Zhang

Research output: Contribution to journalArticlepeer-review


We establish two precise asymptotic results on the Birkhoff sums for dynamical systems. These results are parallel to that on the partial sums of independent and identically distributed random variables previously obtained by Hsu and Robbins, Erdös, Heyde. We apply our results to the Gauss map and obtain new precise asymptotics in the theorem of Lévy on the regular continued fraction expansion of irrational numbers in (0, 1).

Original languageEnglish
Pages (from-to)7095-7108
Number of pages14
Issue number10
Publication statusPublished - 2021 Oct


  • Continued fraction
  • Expanding Markov interval maps
  • Lévy’s theorem
  • Precise asymptotics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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