Stern-Brocot pressure and multifractal spectra in ergodic theory of numbers

M Kesseböhmer, Bernd O Stratmann

Research output: Contribution to journalArticlepeer-review


In this note we apply the general multifractal analysis for growth rates derived in [10], and show that this leads to some new results in ergodic theory and the theory of multifractals of numbers. Namely, we consider Stern–Brocot growth rates and introduce the Stern–Brocot pressure P. We then obtain the results that P is differentiable everywhere and that its Legendre transformation governs the multifractal spectra arising from level sets of Stern–Brocot rates.
Original languageEnglish
Pages (from-to)77-84
JournalStochastics and Dynamics
Issue number1
Publication statusPublished - Mar 2004


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