Abstract
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
behaviour 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 the entropy and Lyapunov spectra.
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
behaviour 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 the entropy and Lyapunov spectra.
| Original language | English |
|---|---|
| Journal | Fundamenta Mathematicae |
| Publication status | Accepted/In press - 22 Jan 2020 |
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Cite this
Jordan, T. M., & Michal, R. (Accepted/In press). Birkhoff spectrum for piecewise monotone interval maps. Fundamenta Mathematicae.