  In this note we study the multifractal spectrum of Lyapunov exponents for
interval maps with infinitely many branches and a parabolic fixed point. It
turns out that, in strong contrast with the hyperbolic case, the domain of the
spectrum is unbounded and points of non-differentiability might exist.
Moreover, the spectrum is not concave. We establish conditions that ensure the
existence of inflection points. We also study the thermodynamic formalism for
such maps. We prove that the pressure function is real analytic in a certain
interval and then it becomes equal to zero.
