Big Birkhoff sums in $d$-decaying Gauss like iterated function systems

Lingmin Liao, Michał Rams Studia Mathematica MSC: Primary 11K50; Secondary 37E05, 28A80. DOI: 10.4064/sm201031-23-8 Published online: 26 November 2021

Abstract

The increasing rate of the Birkhoff sums in infinite iterated function systems with polynomial decay of the derivative (for example the Gauss map) is studied. For different unbounded potential functions, the Hausdorff dimensions of the sets of points whose Birkhoff sums share the same increasing rate are found.

Authors

  • Lingmin LiaoUniversité Paris-Est Créteil
    CNRS, LAMA
    F-94010 Créteil, France
    and
    Université Gustave Eiffel, LAMA
    F-77447 Marne-la-Vallée, France
    e-mail
  • Michał RamsInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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