Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches

Johannes Jaerisch, Hiroki Takahasi

Research output: Contribution to journalArticlepeer-review

Abstract

For a Markov map of an interval or the circle with countably many branches and finitely many neutral points, we establish conditional variational formulas for mixed multifractal spectra of Birkhoff averages of countably many observables, in terms of the Hausdorff dimension of invariant probability measures. Using our results, we are able to exhibit new fractal-geometric results for backward continued fraction expansions of real numbers, answering in particular a question of Pollicott. Moreover, we establish formulas for multi-cusp winding spectra for the Bowen-Series maps associated with finitely generated free Fuchsian groups with parabolic elements.

Original languageEnglish
Article number107778
JournalAdvances in Mathematics
Volume385
DOIs
Publication statusPublished - 2021 Jul 16

Keywords

  • Backward continued fraction expansion
  • Bowen-series maps
  • Dimension theory
  • Mixed multifractal spectra
  • Neutral periodic points
  • Non-uniformly expanding Markov maps

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches'. Together they form a unique fingerprint.

Cite this