Birkhoff spectrum for piecewise monotone interval maps

Thomas M Jordan, Rams Michal

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

For piecewise monotone, piecewise continuous interval maps we look at Birkhoff spectra for regular potential functions. This means considering the Hausdorff dimension of the set of points for which the Birkhoff average of the potential takes a fixed value. In the uniformly hyperbolic case we obtain complete results, in the case with parabolic behavior we are able to describe the part of the sets where the lower Lyapunov exponent is positive. In addition we give some lower bounds on the full spectrum in this case. This is an extension of work of Hofbauer on entropy and Lyapunov spectra.
Original languageEnglish
Pages (from-to)203-223
JournalFundamenta Mathematicae
Volume252 (2021)
Early online date7 Aug 2020
DOIs
Publication statusE-pub ahead of print - 7 Aug 2020

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