  For piecewise monotone 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.
