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Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2022

On the multifractal spectrum of weighted Birkhoff averages

Abstract

In this paper, we study the topological spectrum of weighted Birkhoff averages over aperiodic and irreducible subshifts of finite type. We show that for a uniformly continuous family of potentials, the spectrum is continuous and concave over its domain. In case of typical weights with respect to some ergodic quasi-Bernoulli measure, we determine the spectrum. Moreover, in case of full shift and under the assumption that the potentials depend only on the first coordinate, we show that our result is applicable for regular weights, like Möbius sequence.
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Dates and versions

hal-03534271 , version 1 (19-01-2022)

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Balázs Bárány, Michaƚ Rams, Ruxi Shi. On the multifractal spectrum of weighted Birkhoff averages. Discrete and Continuous Dynamical Systems - Series A, 2022, ⟨10.3934/dcds.2021199⟩. ⟨hal-03534271⟩
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