  We survey some results on non-uniform hyperbolicity, geometric pressure and
equilibrium states in one-dimensional real and complex dynamics. We present
some relations with Hausdorff dimension and measures with refined gauge
functions of limit sets for geometric coding trees for rational functions on
the Riemann sphere. We discuss fluctuations of iterated sums of the potential
$-t\log |f'|$ and of radial growth of derivative of univalent functions on the
unit disc and the boundaries of range domains preserved by a holomorphic map
$f$ repelling towards the domains.
